Low-energy Coulomb excitation of $^{62} $ Fe and $^{62} $ Mn ...

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Oct 27, 2015 - the zero-angle position of the Miniball array. A new transition was ...... A 660, 3 (1999). 60. D. Pauwels, (private communications) (2014). 61.
EPJ manuscript No. (will be inserted by the editor)

Low-energy Coulomb excitation of in-beam decay of 62Mn

62

Fe and

62

Mn following

arXiv:1506.06672v2 [nucl-ex] 27 Oct 2015

L. P. Gaffney1,a,b , J. Van de Walle1,2 , B. Bastin1,3 , V. Bildstein4,c , A. Blazhev5 , N. Bree1 , J. Cederk¨all6 , I. Darby7 , H. De Witte1 , D. DiJulio6 , J. Diriken1,8 , V. N. Fedosseev2 , Ch. Fransen5 , R. Gernh¨auser5 , A. Gustafsson2 , H. Hess5 , M. Huyse1 , N. Kesteloot1,8 , Th. Kr¨ oll9 , R. Lutter10 , B. A. Marsh2 , P. Reiter5 , M. Seidlitz5 , P. Van Duppen1 , D. Voulot2 , N. Warr5 , F. Wenander2 , K. Wimmer4,d , and K. Wrzosek-Lipska1,11 1 2 3 4 5 6 7 8 9 10 11

KU Leuven, Instituut voor Kern- en Stralingsfysica, 3001 Leuven, Belgium CERN-ISOLDE, CERN, CH-1211 Geneva 23, Switzerland GANIL CEA/DSM-CNRS/IN2P3, Boulevard H. Becquerel, F-14076 Caen, France Physics Department E12, Technische Universit¨ at M¨ unchen, D-85748 Garching, Germany Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, 50937 K¨ oln, Germany Physics Department, University of Lund, Box 118, SE-221 00 Lund, Sweden University of Jyvaskyla, Department of Physics, FI-40014 University of Jyvaskyla, Finland Belgian Nuclear Research Centre SCK•CEN, Boeretang 200, B-2400 Mol, Belgium Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, D-64289 Darmstadt, Germany Ludwig-Maximilians-Universit¨ at-M¨ unchen, Schellingstraße 4, 80799 M¨ unchen, Germany Heavy Ion Laboratory, University of Warsaw, PL-00-681 Warsaw, Poland Published: 28th October 2015 Abstract. Sub-barrier Coulomb-excitation was performed on a mixed beam of 62 Mn and 62 Fe, following in-trap β − decay of 62 Mn at REX-ISOLDE, CERN. The trapping and charge breeding times were varied in order to alter the composition of the beam, which was measured by means of an ionisation chamber at the zero-angle position of the Miniball array. A new transition was observed at 418 keV, which has been tentatively associated to a (2+ , 3+ ) → 1+ g.s. transition. This fixes the relative positions of the β-decaying 62 4+ and 1+ states in 62 Mn for the first time. Population of the 2+ Fe and the cross1 state was observed in section determined by normalisation to the 109 Ag target excitation, confirming the B(E2) value measured in recoil-distance lifetime experiments. PACS. 25.70.De Coulomb excitation – 21.10.Ky Electromagnetic moments – 29.38.Gj Reaccelerated radioactive beams – 27.50.+e 59 ≤ A ≤ 89

1 Introduction Shell-closures in nuclei are known to evolve when moving away from the line of β stability, with vanishing or newly appearing energy gaps [1–7]. At N = 20, this changing shell-structure leads to an “island of inversion” [7, 8], whereby the usual spherical mean-field gap between the sd and f p shells is eroded by strong quadrupole correlations. As a consequence, deformed intruder states become the major component of the ground state around 32 Mg [9]. The spherical structures then appear as excited 0+ states a

Corresponding author: [email protected] Present address: School of Engineering, University of the West of Scotland, Paisley PA1 2BE, United Kingdom c Present address: Department of Physics, University of Guelph, Guelph, ON, Canada N1G 2W1 d Present address: Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan b

in the even-even members of this so-called island [10], leading to what can also be described as a type of shape coexistence [11]. This unexpected increase of quadrupole collectivity at shell closures is not only restricted to the N = 20 region, however. Indicated by the high-lying 2+ 1 + 68 Ni [12, 13], the state and low B(E2; 2+ 1 → 01 ) value in weak N = 40 sub-shell gap vanishes with the removal or addition of only a couple of protons [14, 15]. Excited 0+ states have been identified in 68 Ni [16–18] and are suggested to be deformed intruder configurations in recent Monte Carlo Shell Model (MCSM) calculations [19]. The coexistence of these shapes [11, 18, 19] leads to the proposition of a new island of inversion around 64 Cr, described in shell-model calculations using the new LNPS effective interaction [20]. In the Cr isotopic chain with 32 < N < 40, a gradual onset of quadrupole collectivity is observed [21– 25]. Recent B(E2) measurements were performed in the neutron-rich Fe isotopes using the recoil-distance lifetime

2

L. P. Gaffney et al.: Coulomb excitation of

technique [26, 27] and intermediate energy Coulomb excitation [24], showing a sudden increase in deformation at N = 38. In this experiment, low-energy Coulomb excitation of 62 Fe can provide a confirmation of this observation. In the odd-mass and odd-Z nuclei about 64 Cr, the role of the νg9/2 orbital can be mapped more directly. Shellmodel calculations [28] have shown the importance of this intruder orbital as neutron excitations across N = 40 play a key role in the most neutron-rich Mn isotopes. Recent experiments have identified negative-parity structures associated with occupancy of the νg9/2 orbital [29] in a number of these nuclei. However, the behaviour of these states with respect to the ground-state configuration is limited in 62 Mn due to the unknown positioning of the isomer and ground-state levels. It has recently been confirmed that the two β-decaying states have I π = 1+ and 4+ [30], but their relative positions remain unknown. With the Coulomb-excitation technique, it has been possible in this paper to identify a new state built upon the longerlived 4+ state in 62 Mn. Here we report on its identification and propose the ordering and relative energies of the two β-decaying states; in turn we also fix the energy of the negative parity states identified in Ref. [29].

2 Experimental Details Extraction of refractory and refractory-like elements in atomic form from ISOL (Isotope Separator On-Line) targets is very slow and inefficient. The atoms first need to diffuse through the target matrix to the surface and then desorb before reaching the ion source. Many elements will undergo this process quickly and may collide with the walls of the heated transfer line (≈ 2000◦ C) many times en route to the ion source, adsorbing and desorbing quickly each time. The biggest bottle neck in the extraction of refractory-like elements, such as Fe, comes from slow desorption [31]. This may be seen as a benefit where isobaric purity is required, but certainly not when beams of shortlived isotopes of such troublesome elements are desired. Fast and chemically-independent extraction is planned at future facilities with new gas-catcher and laser-ionisation coupled systems [32]. Gas-catchers are currently employed at the CARIBU experiment at ANL [33], producing beams of Cf fission products that have been reaccelerated for Coulomb-excitation studies. With the thick solid target at ISOLDE however, alternative techniques than direct extraction have to be explored, such as forming volatile gaseous compounds [34]. Recently, the technique of in-trap decay was pioneered at REX-ISOLDE using 61 Mn as a test case to produce a beam of the refractory-like 61 Fe [35]. Following these successful tests, a further experiment on 62 Mn/Fe was performed and is described here. The manganese beams are produced at ISOLDE by proton-induced fission of uranium, driven by a 1.4 GeV proton beam from the CERN’s PS Booster, impinging on a thick UCx target. Element-selective ionisation takes place with the Resonance Laser Ionisation Laser Ion Source (RILIS) [14, 36, 37] and the Mn1+ ions are extracted from the ion source with a 30 kV potential and mass separated

62

Fe and

62

Mn

with the General Purpose Separator (GPS). After this the beam is bunched in REX-TRAP [38, 39] and released into the charge breeder, REX-EBIS [38, 39], finally attaining a charge state of 21+ . The latter stage is required in order to achieve a mass to charge ratio of A/q < 4.5 for injection to the REX linear accelerator [40]. The distribution of charge states is sensitive to the charge-breeding time. Both the trapping and charge-breeding times were varied during the experiment in order to investigate the production of 62 Fe via the “in-trap” method (see Section 2.1). Ultimately, the beam was delivered to the Miniball array [41] at a final energy of 2.86 MeV/u. Here it was either incident on a 4 mg/cm2 -thick 109 Ag target to induce Coulomb excitation, or into the ionisation chamber, filled with CF4 gas and backed by a thick silicon detector, to monitor the beam composition [41]. 2.1 In-trap decay During the trapping and charge-breeding stages, the 62 Mn ions are held for varying time periods from 28 ms to 740 ms. At a number of these timing settings, the beam composition was measured in the ∆Egas -ESi telescope of the ionisation chamber. An example of the ∆Egas spectra are shown in Fig. 1. The energy loss in the gas is proportional to the Z of the projectile and is sensitive to the gas conditions such as pressure. Good optimisation of these conditions allowed for a clear separation of Z = 25, 26 and therefore the ratio of manganese to iron in the beam. Under idealised conditions, i.e. no losses during trapping and charge breeding and a constant rate of injection to REX-TRAP, this ratio of manganese and iron can be calculated using simple mother-daughter decay laws. Assuming the injection of the high-spin state of 62 Mn(T1/2 = 671(5) ms [14]) into the trap (see Section 3.2) at a constant rate, its decay and the grow-in and decay of 62 Fe(T1/2 = 68(2) s [42]) can be integrated over the total trapping time, tT . Z tT T NMn 1 = e−λMn t dt, (1) N0 tT 0 Z tT T  1 λMn NFe e−λMn t − e−λFe t dt, (2) = N0 tT 0 λFe − λMn T where N0 and NMn are the numbers of Mn+ ions injected T into and extracted from the trap, respectively, and NFe T is the number of Fe+ ions extracted from the trap. NMn T and NFe are then treated as the number of the respective ion species that are injected into the EBIS chargestate breeder, where further decay occurs while the beam is confined for the charge breeding time, tE . E NMn NT = Mn e−λMn tE , N0 N0 E NT NFe = Fe e−λFe tE N0 N0  NT λMn + Mn e−λMn tE − e−λFe tE . N0 λFe − λMn

(3)

(4)

62 6262 62 62 L.L. P.P. Ga↵ney Coulomb excitation FeFeand Mn L. P. Gaffney et al.: Coulombofexcitation of 62 Fe following and Mnin-beam Ga↵neyetetal.: al.:Low-energy Low-energy Coulomb excitation of 62 and Mn following in-beamdecay decayofof 62Mn Mn

2525 Counts per 4 arb. units Counts per 4 arb. units

2020

E

Mn 25) Mn(Z(Z== 25)

Fe/Mn ratio Fe/Mn ratio

1515 1010 55

00 3535 3030 2525 2020

0.9 0.9 0.8 0.8

tTt ==3030ms ms T tEt ==2828ms ms

Mn 25) Mn(Z(Z== 25)

tTtT==400 400ms ms tEtE==348 348ms ms

FeFe(Z(Z==26) 26)

0.7 0.7 0.6 0.6

333

tTt ==3030ms ms T tTt ==300 300ms ms T tTt ==400 400ms ms T

0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 00 00

0.05 0.05 0.1 0.1 0.15 0.15 0.2 0.2 0.25 0.25 0.3 0.3 0.35 0.35 0.4 0.4 Charge Chargebreeding breedingtime, time,tEtE[s][s]

62 to 62 Mn in the beam, measured experMn Fig. 3. Ratio of Fetoto 62 Mnininthe thebeam, beam,measured measuredexperexperimentally in the ionisation chamber, as a function ofof charge imentally ininthe ionisation chamber, asasaafunction charge imentally the ionisation chamber, function of charge 1010 breeding time, time, tE.. Theoretical Theoretical curves for different trapping breeding breeding time,tEtE . Theoreticalcurves curvesfor for di↵erent di↵erent trapping trapping times, t , are also shown in red, black and blue corresponding T times, t , are also shown in red, black and blue corresponding T 55 times, t T , are also shown in red, black and blue corresponding 30ms, ms,300 300 ms ms and and 400 400 ms, ms, respectively. respectively. It that toto ItItisisisassumed assumed to3030 ms, 300 ms 62 and ms, respectively. assumedthat that the halflife of the Mn400 component is 671 ms, corresponding 00 6262 the halflife ofofthe Mn component isis671 ms, corresponding the halflife the Mn component 671 ms, corresponding 500 1000 1500 2000 2500 3000 500 1000 1500 2000 2500 3000 to the high-spin β-decaying state [14]. totothe thehigh-spin high-spin -decaying -decayingstate state[14]. [14]. EE[arb. units] [arb. units] Fig. 2.2.1. E∆E asas measured Fig. Esignal signal measured arbitrary units fromthe the Fig. signal as measuredinin inarbitrary arbitraryunits unitsfrom from the EE TT NN FeFe NN ionisation chamber, proportional toto placed mm downstream from the tarE ionisation chamber, proportional energy lossofofthe beam, CD detector, ionisation chamber, proportional toenergy energyloss thebeam, beam, == FeFe e e FeFetEt32.5 N N E, for two di↵erent trapping and charge-breeding settings. [41]. 00 0 0 This corresponds to an angular coverage N N E, for settings. get position ∆E, fortwo two di↵erent different trapping trapping and and charge-breeding charge-breeding settings. (4) (4) TT Top panel: 3030 msms trapping time, tTtt,TTand 2828ms of 15.6◦Mn –51.6◦ and in the centre-of-mass Top panel: trapping time, ,, and mscharge-breeding charge-breeding Top panel: 30 ms trapping time, and charge-breeding in the lab frame NN tEtE tEtE Mn Mn Fe Mn ◦ Mn Mn Fe ◦ + e e . + of 24.3 –148.9 . For e the evaluation e . the time, tEt.EtBottom panel: tTttT= 400 msms and (CoM) frame of time, . .Bottom panel: 400 and 348ms mstime. time. time, Bottom panel: = 400 ms andtEtE==348 ms. E T= N

1515

62 gas shown inin2Fig. energy ininofthe isis62 proporshown Fig.2.2.The The energyloss loss the proporFigure shows the calculated ratio Fegas and Mn for tional totothe Z Zofofthe projectile and totothe tional the the projectile andisto issensitive sensitive thegas gas different trapping times, compared the experimentally conditions such asaspressure. optimisation ofofis these determined values. One canGood see that the behaviour genconditions such pressure. Good optimisation these conditions allowed forfora and 2626 erally well understood anseparation appreciable of25, iron conditions allowed aclear clear separationofamount ofZZ==25, and therefore the can be accumulated inofmanganese the beam. to For theinlongest trapand therefore theratio ratioof manganese toiron iron inthe thebeam. beam. pingidealised times, theconditions, iron-to-manganese content is generally less Under trapping Under idealised conditions,i.e. i.e.nonolosses lossesduring during trapping than expected. Thisand may due in part to of space-charge efand charge breeding rate and charge breeding andabe aconstant constant rate ofinjection injectionto to fects, whichthis limit theof number of ionsand that cancan be fed into REX-TRAP, iron REX-TRAP, thisratio ratio ofmanganese manganese and iron canbe becalcalthe trap insimple each bunch. Furthermore, thelaws. recoil energy culated using mother-daughter decay culated using simple mother-daughter decay laws.AssumAssumofthe the Fe ions of following the β-decay process may1/2 cause ing state ofof6262 Mn(T ing theinjection injection ofthe thehigh-spin high-spin state Mn(T 1/2== losses in[14]) the trap. This istrap highlighted by the data point at 671(5) msms into atata aconstant rate, itsits decay 671(5) [14]) intothe thetrap constant rate, decay 62 62 t = 300 ms and t = 28 ms that lies close to the value Tthe Edecay and and thegrow-in grow-inand and decayofof Fe(T Fe(T 68(2)s s[48]) [48]) 1/2 1/2==68(2) taken with a much shorter trapping time of tTtTt= can integrated over thetotal total trapping time, can bebeintegrated over the trapping time, .T .30 ms. While it appears as though longer charge breeding times Z Z tT T Tincrease are preferableN toN ratio, the efficiency of 1 1thetTFe/Mn Mn t t Mn Mn (1) == e e Mn dt,dt, (1) achieving the correct charge state for injection to the REX NN tt 00 0 0 accelerator reduces andT T an overall loss of beam intensity Z ZtTover. tT begins Additionally, the charge distributions T T to take NN Mn Mn t t t t FeFe =1 1 Mn e FeFe dt, (2) of Mn=and Fe ions in REX-EBIS will bee different meaning e e Mn dt, (2) N t N t 0 T Fe Mn 0 T Fe Mn 0 0 that these effects cannot be separated.

T T are the numbers of Mn whereNN ionsinjected injected where NN are the numbers of Mn+ +ions 0 and 0 and Mn Mn TT intoand andextracted extractedfrom fromthe thetrap, trap,respectively, respectively,and andNN into FeFe + T + T 2.2 Coulomb excitation thenumber numberofofFeFe ions ionsextracted extractedfrom fromthe thetrap. trap.NN is isthe Mn Mn T T are then treated as the number of the respecand N and NFeFeare then treated as the number of the respec109 tive ionspecies species that areinjected intothe the EBISchargechargeWith the Ag target ininjected place, into “safe” Coulomb excitative ion that are EBIS state breeder, where further decay occurs while the beam tion [43] takes place and the scattered projectiles and restate breeder, where further decay occurs while the beam coiling target nuclei are detected intime, atime, compact-disc-shaped confined thecharge charge breeding is isconfined forforthe breeding tEt.E . Double-Sided Silicon Strip Detector (DSSSD), the so-called EE TT NN t Mn NN Mn MnMn Mn Mn = (3) = e e tE ,E , (3) N 0 0 NN N 0 0

62 Fig. 3. 2. Ratio Ratio of of 62 Fe 62 Fig. Fe

N 0 FeFe Mn Mn cross-section the 0inner-most strip is not used since it was 6262 de-excitation broken one of the four quadrants. The γfor Figure the calculated ratio Fe Figure3on 3shows shows the calculated ratioofof Feand and6262Mn Mnfor rays are detected the HPGe crystals Miniball, which di↵erent trapping compared totoofthe experimental di↵erent trappingintimes, times, compared the experimental each have six-fold segmentation, arranged into eight is triple determined values. One determined values. Onecan cansee seethat thatthe thebehaviour behaviour isgengenclusters. Prompt and random coincidences between partierally well understood and an appreciable amount of erally well understood and an appreciable amount ofiron iron cle and γ-ray eventsinare built in the described in can beam. For the trapping canbe beaccumulated accumulated inthe the beam. Formanner thelongest longest trapping Ref. [44]. angles greater than 48◦ in times, the iron isisgenerally less expected. times, theFurthermore, ironcontent contentfor generally less than than≈ expected. the frame, both partners for e↵ects, ae↵ects, given which CoM This may bebedue ininscattering part Thislab may due parttotospace-charge space-charge which scattering angle will be inside of the CD range (see Fig-inin limit limitthe thenumber numberofofions ionsthat thatcan canbe befed fedinto intothe thetrap trap ure Therefore, two-particle coincidences inofthe this range each bunch. Furthermore, the each3). bunch. Furthermore, therecoil recoilenergy energyof theFe Feions ions are also considered in the analysis. following followingthe the -decay -decayprocess processmay maycause causelosses lossesininthe thetrap. trap. 2 Aisis relatively thick target (4.0point mg/cm )tTtwas used in and orThis highlighted by the This highlighted by thedata data pointatat 300ms ms and T==300 der to increase the yield, which resulted in poor energy tEtE==2828ms msthat thatlies liesclose closetotothe thevalue valuetaken takenwith withaamuch much resolution of the time scattered In While turn, not shorter appears shortertrapping trapping timeofoftTtparticles. 30ms. ms. Whileitititwas appears T ==30 tolonger cleanly resolve the scattered projectiles andto asthough though longer charge breeding timesare are preferable to aspossible charge breeding times preferable target recoils in terms of energy and laboratory angle, the as increase theMn/Fe Mn/Fe ratio, theefficiency efficiency achieving the increase the ratio, the ofofachieving can be seen in Figure 4. heavier-mass target species that correct charge statefor forAinjection injection the REX accelerator correct charge state totothe REX accelerator still provides the relative normalisation via observable exreducesand andan anoverall overallloss lossofofbeam beamintensity intensitybegins beginstototake take reduces citation would have allowed a greater separation of the two over.Additionally, Additionally,the thecharge chargedistributions distributionsofofMn Mnand andFe Fe over. kinematic solutions will inwill energy. Nevertheless, under thethese asionsininREX-EBIS REX-EBIS bedi↵erent di↵erent meaning that these ions be meaning that sumption thatbebe either a projectile-like or recoil-like particle e↵ectcannot cannot separated. e↵ect separated. is detected, it is possible to solve the two-body kinematic problem for the other scattering partner. It appears as though the detected energy is systematically lower than 2.2 Coulombexcitation excitation 2.2 thatCoulomb expected from the calculations (see Fig. 4). The calibration of 109 the detector used a triple-α source of 239 Pu241 243109 Ag With the target place, “safe” Coulomb excitaWith the target ininplace, “safe” Coulomb excitaAmCm Ag with energies around 5 MeV and the extion[49] [49]takes takes placeand andthe thescattered scattered projectiles andAt retion and retrapolation to place higher energies may well projectiles be non-linear. coiling target nuclei are detected in a compact-disc-shaped coiling target nuclei detected in a compact-disc-shaped the velocities used inare this experiment, the Doppler shift of Double-Sided Silicon Strip Detector(DSSSD), (DSSSD), theso-called so-called Double-Sided Silicon Strip Detector the γ-rays emitted in flight is dominated by the angular comCDdetector, detector,placed placed32.5 32.5mm mmdownstream downstreamfrom fromthe thetartarCD getposition position[47]. [47].This Thiscorresponds correspondstotoan anangular angularcoverage coverage get

Counts Counts per per 10 10 keV keV Counts per 10 keV

Recoiling target angle angle [deg] [deg] Recoiling target

90 90 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 00 00

80 80 80 60 60 60 40 40 40 20 20 20 000

-20 -20 -20 20 20

40

60 80 100 120 60 80 100 120 Scattered Scattered projectile projectileangle angle[deg] [deg] Fig. 3. 3. Kinematic Kinematic relationship relationship of Fig. 3. Kinematic of laboratory scattering angles Fig. of laboratory laboratoryscattering scatteringangles angles for a mass A = 62 projectile impinging on a for aa mass mass A = 62 projectile impinging mass AA= ==109 109 for impinging on on aa mass massA 109 target at at an an energy energy of of 2.86 2.86 MeV/u. target at an MeV/u. It is assumed that there isis target MeV/u. It It is is assumed assumedthat thatthere thereis anexcitation excitation of of 0.877 0.877 MeV. MeV. The an excitation The horizontal horizontal and vertical dashed an horizontaland andvertical verticaldashed dashed linesrepresent represent the the limits limits of of lines represent the limits detection in the CD detector. Only lines of detection detection in in the theCD CDdetector. detector.Only Only for a small range of scattering angles are both the projectile for a small range of scattering angles are both the and for a small range of scattering angles are both theprojectile projectileand and recoil expected expected to to be be in in the the range of detection simultaneously. recoil recoil expected to be in the range range of of detection detection simultaneously. simultaneously.

Counts per 1 keV Counts per 1 keV Counts per 1 keV

62 62 6262 6262 62 Mn L. P. Ga↵ney et al.: Low-energy Coulomb excitation Fa L. P. Ga↵ney et al.: Low-energy Coulomb excitation Fean L. P. P. Ga↵ney Ga↵neyet etal.: al.:Coulomb Coulombexcitation excitationof of62 Fe and Mn L. P. Gaffney et al.: Coulomb excitation of Fe and L. P. Ga↵ney et al.: Low-energy Coulomb excitation ofof62ofFe L. Fe and Mn

444

5005 500

4004 400

3003 300

2002 200

-40 -40 -40 500 500 500

Counts [1/MeV/deg.] Counts [1/MeV/deg.]

Energy Energy[MeV] [MeV]

1001 100 600 700 800 900 1000 1100 1200 600 600 700 700 800 800 900 900 1000 10001100 11001200 1200 Energy [keV] Energy [keV] Energy [keV] 00 Fig. 6. Background-subtracted -ray spectrum showing thethe 6. Background-subtracted -ray spectrum the Fig. 5.5. Background-subtracted γ-ray spectrum showing the Fig. 5. Background-subtracted showing the Fig. 6. Background-subtracted -ray spectrum showing Background-subtracted the + ++ 62 + 62 62 2+ ! transition ofof62 FeFe following Coulomb excitation onon ++ 62 2877 ! 00+ of Fe following Coulomb excitation on keV →! transition of FeFe following Coulomb excita62 877-keV ! 00+1 + transition of Fe following Coulomb excita1877-keV 1122transition 21+ transition following Coulomb excitation 2+ of following Coulomb excita1 ! 0111 2 101 transition 109 2 109 1 2 109 2 109 aa4.0 4.0 mg/cm -thick Ag target. Data atat all trapping and 2 ation mg/cm -thick Ag Data at all trapping and on a 4.0 mg/cm -thick Agtarget. Data at all trapping 2109 109 tion on Ag Data at all trapping 4.0 -thick-thick Agtarget. target. Data all trapping and Fig. 7. tion onamg/cm a4.0 4.0mg/cm mg/cm -thick Agtarget. target. Data at all trapping 7. charge-breeding settings areare summed this spectrum, al- Fig. charge-breeding settings are summed inin this spectrum, aland charge-breeding settings are summed in this spectrum, aland charge-breeding settings summed in this spectrum, alFig. charge-breeding settings are summed in this spectrum, al- showing and charge-breeding settings are summed in this spectrum, althelongest longesttimes. times.Note Notehere here showing the longest times. Note here though 75% 75% data data was was taken takenwith withthe the longest times. Note here though showit the longest longest times. times. Note Note here here ping though 75% data was taken applied with the and and becauseof ofthe theambiguity ambiguity ping applied because of the ambiguity that no no Doppler Doppler correction correctionisisapplied applied because of the ambiguity that because ping a applied because because of of the the ambiguity ambiguityalthough no Doppler correction is applied althoug ofthat projectileand recoil-like events. of projectileand recoil-like events. projectileThis leads to the wide peak projectileand recoil-like events. This leads to the wide peak altho projectile- and and recoil-like recoil-likeevents. events.This leads to the wide peaktra of projectile160 areD are 102 2 with an an irregular irregular(non-Gaussian) (non-Gaussian)peak peakshape. shape.The Thestructure structureatat tratra with 160 Projectiles a 10 with an irregular (non-Gaussian) peak shape. The structure atlike Projectiles par part ≈ 670 670 keV keV isis likely likely to to be be the the Compton Compton edge edgeofofthe the877 877keV keV likelike 140 ⇡ Recoils p 140 ⇡ 670 keV is likely to be the Compton edge of the 877 keV Recoils particle( the fraction fraction of of the the observed observed de-excitation de-excitationintensity intensityininthe the particle the peak. peak. partic 120 the fraction of the observed de-excitation intensity in the peak. 62 62 (red; (red;blu bl target target associated associated with with Fe Fe can canbe bededuced deduced[37]: [37]: 120 (red; target associated with 62 Fe can be deduced [37]: peak isissy peak 100 Table 1. Experimental intensities of -ray transitions followpeak 100 from the from the 62of Table Experimental intensities -raytransitions transitions follow11mixed of 10 Table 1.1.Experimental γ-ray following Coulomb excitation ofintensities the Mn/Fe beam on a 109 Ag 80 from ⇣ ⌘ ⇣ ⌘ F = 0.36(3), (5) 62= 109 F = = 0.36(3), (5) 1 10 62 109 Fe Fe and when and whe 62 62 ing Coulomb excitation of the mixed Mn/Fe beam on a Ag ing Coulomb excitation of the mixed Mn/Fe beam on a Ag ( Mn) ( Mn) 80 t ⇣ ⌘ t target. A correction for R the relative efficiency of the Miniball (5) and w FFe =11+ = 0.36(3), + RMn 62 Mn) Mn relative (Fe) ((62 418keV keV t62 Fe)efficiency 60 tt target. correction the efficiencyof of the Miniball418 target. AAcorrection relative the Miniball array, normalised to 877.3 keV, along 1for +forthe R 62 with its uncertainty is inMn 418 k 60 t ( Fe) array, normalised to 877.3 along with its uncertainty is inarray, normalised to 877.3 keV, with its uncertainty is cluded. The assignment of the 418-keV transition is discussed 40 62 (The (62Fe) Fe) ttThe cluded. assignment ofratio the418 418-keV transition discussed included. the keV transition is is discussed 40 where and is theof of cross sections of exciting in Section 3.2. 62 assignment where 62 62 ( Mn) ( Fe) and is the ratio of cross sections of exciting tt (t Mn) 20 1 where and is the ratio of cross sections of exciting Section 3.2. inin Section 3.2. 62 62 62 62 62 ( interest Mn) tof withres re the the by 20 the state state of interest in thetarget, target, byaa Fe Feor or IMn Mnbeam. beam. with 1 Energyin [keV] Transition 62 62 0 the state of interest in the target, by a Fe or Mn beam. set ofofE2 setwith E Calculated using the Coulomb-excitation code, gosia [52, Energy [keV] Transition Energy [keV] Transition I Calculated using the Coulomb-excitation code, gosia [52, γI 15 20 25 30 35 40 45 50 62 0 setofoo Feratio 877.3 2+ 0+ 210(40) Calculated using the Coulomb-excitation code, gosia [52, levels 53], this is 0.9915 for the 3/2 at 311 keV 1 ! 1 state levels 15 20 25 30 Laboratory 35 40 angle 45 [deg.] 50 53], this ratio is 0.9915 for the 3/2 state at 311 keV 1 + + 6262 + 109 Fe 877.3 01101+ 210(40) Fe 877.3 2! 210(40) 109 Ag 3/2 1/2 1520(40) levels 109Ag. 1additional this ratio 311.4 is 0.9915 3/2 at 311 inin keVcial 1→! 1 state vers Laboratory angle [deg.] in53], Secondly, there isfor an21the component cial ver Ag. component 1 − 109 109 Secondly, there is an−additional 109 Fig. 4. (Color online) Detected particle events in the CD in 109 Ag 311.4 3/2 → 1/2 1520(40) Ag 311.4 3/2 ! 1/2 1520(40) Ag 415.2 5/2 1/2 2300(60) cial 1! 1 1 5/2 1 tionally, in Ag. Secondly, there is an additional component in 1 1 the Doppler-broadened -ray peak of the ! 1/2 tionally the Doppler-broadened -ray peak of the 5/2 ! 1/2 1 1 − − 109 109 Fig. 4. (Color online) Detected particle events in the CD detector plotted as a function of angle and energy in the labo1 1 + 62 + + Fig. 4. (Color online) Detected particle events in the CD Ag 415.2 → 1/2 2300(60) Ag 109 415.2 5/2 1/2 2300(60) Mn 418(2) (25/2 31 peak 1of 970(50) tiona 1) ! 11 1the the Doppler-broadened -ray 5/2 di↵erences (3/2 transition in 109Ag Ag around around415 415+,keV. keV. Using the di↵erences 2 2, ,5 1 ! 1/21 (3/2 + +the 6262 in + +Using ratory frame of reference. An of angle-dependent energy threshdetector plotted as of angle angle and and energy energy inthe the labo- transition + detector plotted as a a function function in laboMn (2 , 3 ) → 1 970(50) 109418(2) Mn 418(2) (2 , 3 ) ! 1 970(50) 1 (3/2 1 the calc transition in Ag around 415 keV. Using the di↵erences between peak shape in the Doppler-corrected spectra of the cal2 between peak shape in the Doppler-corrected spectra of old hasframe been of applied in software to remove low-energy events ratory reference. angle-dependent energy threshthreshratory frame An angle-dependent energy for aasim the Figure 7 a second component at 418-keV emerges, assobetween peak shape in the Doppler-corrected spectra of for sic Figure 7 a second component at 418-keV emerges, assocaused by noise on the detector. The two shaded regions show old has been applied in software to remove low-energy events old has been software to remove low-energy events the targ peak) is large because of this subtraction. An additional for a ciated with the projectile. Its intensity can be extracted Figurewith 7 a the second component at 418-keV emerges, asso- the tar the calculated of the projectile and recoils for show elasprojectile. Its intensity can be extracted caused by on the detector. detector. The two two shaded shaded regions show ciated caused by noise noisebehaviour The regions 8.1% uncertainty is calculated from the uncertainty in the set of no the t peak) is large because of this subtraction. An additional by subtracting the true 5/2 ! 1/2 -transition intensity ciated with the projectile. Its intensity can be extracted set of n tic scattering including energy loss in the target. The range is by subtracting the keV true (also 5/211 511 ! 1/2 the projectile and and recoils recoils for forelaselas- region 11 -transition intensity the calculated calculated behaviour of the projectile around of 877 keV associated with thethetensities determination the background normalisation. All of this I (5/2 !1/2 ) 8.1% uncertainty is calculated from the uncertainty in set o determined by the assumption of the reaction at the entrance tensitie I (5/2 !1/2 ) 1 1 by subtracting the true 5/2 ! 1/2 -transition intensity tic loss in in the the target. target. The Therange rangeisis extracted tic scattering scattering including energy loss 1 1 = 1.13, calculated 1 1 the ratio, extracted from from thetotal ratio, = subtraction. 1.13, calculated annihilation is large ofin this An complete II because (3/2 topeak) the uncertainty integrated inor exit of the while the solid line assumes reaction in propagates 11!1/2 11) )the !1/2 determination of the background normalisation. All of this comple tensi I(3/2 (5/2 determined of reaction at entrance determined bytarget, the assumption of the the reaction atathe the entrance 1 !1/2 1 ) + + extracted from the ratio, = 1.13, additional 8.1% uncertainty is calculated from thecalculated uncerin gosia using previously measured matrix elements, and tensity of the 2 ! 0 (shown in Table 1), hindering the 5 in gosia using previously measured matrix elements, and the centre. However, the detector resolution is not considered I (3/2 !1/2 ) uncertainty in the integrated in-served comp served 1 or exit exit of of the the target, while the solid or solid line line assumes assumes aa reaction reactioninin propagates to1 the total 1 1 tainty in of the determination of the background normalisathe “clean” intensity of 311-keV, 3/2 ! 1/2 tran+ +the here, nor is the finite width of the CD-detector strips. precision the cross-section measurement. in gosia using previously measured matrix elements, and the cons the “clean” intensity of the 311-keV, 3/2 ! 1/2 tran1 1 the theserve the centre. centre. However, the detector con the detector resolution resolution isis not not considered considered tensity of the 21 ! 01 (shown in Table 11), hindering 1 tion. All of deduced this propagates toofof the total uncertainty the sition. The intensity the 418-keV transition isis the order tothe extract the cross-section, we 1normalise proj sition. The intensity the transition theIn“clean” intensity of the 3/2 ! 1/2in tranhere, nor nor is is the finite width of the here, the CD-detector CD-detector strips. strips. precision ofdeduced cross-section measurement. thethe proc 1 to + 311-keV, ++418-keV +

ponent and the correction is rather insensitive to changes in the particle ponent and the theenergy. correction is ponent and correction is rather rather insensitive insensitive to to changes changes A background subtraction of the -ray spectra is perin the particle energy. in the particle energy. formed using the randomly-coincident events, normalised A background background subtraction of spectra isisperA subtraction of the the γ-ray -ray spectra perto the intensity ofrandomly-coincident rays emitted following the normalised -decay of formed using the events, formed using 62 62 the randomly-coincident events, normalised Co. of The rays background subtraction is key since to Fe theand intensity to the intensity of γ 62 rays emitted emitted following following the the β-decay -decayofof 62 62 the decay of the Mn mother (scattered into the CD 62 Fe and 62 Co. The background subtraction is key Fe and Co. The62background subtraction is+key since since and the walls of the chamber) will populate the 2 in 1 state the β decay decay of of the the 62 Mn mother (scattered into the CD the Mn mother (scattered into the CD 62 Fe, giving rise to falseofcoincidences with non-Coulomb+ detector and the walls the chamber) will populate the and of the + chamber) will populate theobserved 21 stateinin + + the walls 62 As can be 1 ! 01rise-rays. 2excitation-related in riseFe,to2giving to false coincidences with 62 1Fe,state giving false coincidences with non-Coulomb+ of Fig. 5, the the background-subtracted spectrum + + -ray2+ non-Coulomb-excitation-related → 0 γ-rays. As can 1 As can 1 excitation-related be observed 1 ! 01 of -rays. uncertainty on the2background-subtracted number counts in the region aroundin be observed in the γ-ray spectrum the background-subtracted -ray spectrum of Fig. 5, the 877Fig. keV 511 keV associated with the annihilation of 5, (also the number of region counts in the uncertainty onuncertainty the numberonofthe counts in the around 877 keV (also 511 keV associated with the annihilation

109the integrated of 2target. → (shown in transition Table 1), almost times greater than the 21At ! transition inin is 1cross-section, the excitation of extract the Ag this two isalmost five times greater than the 21+ !001+ transition sition. Theintensity deduced intensity of 0the In five order to the we normalise to the 1 418-keV 1point, InIn62p6 62 + + hindering the precision of the cross-section measurement. 62Fe are (see Table 1), meaning that this must originate from 109 sues encountered. First of all, both components of the Fe (see Table 1), meaning that this must originate from almost five times greater than the 2 ! 0 transition in the excitation of the Ag target. At this point, two iserned 1 1 62 ernedini 62 62 62 Mn. The assignment of transition will 62 beam, Fe and Mn, will give risethis to must excitation of the Mn. The assignment of this this transition will bediscussed discussed In are order to extract the cross-section, we be normalise tothenamelyIn Fe (see Table 1), meaning that originate from sues encountered. First of all, both components of namely erned in A particle-ratio events showed 62Section target. With knowledge the total ofpoint, manganese 62 3.2. 62 109of inbeam, Section 3.2. A search search particle- this showed no the excitation of the target. At twoofno isMn. The assignment of this transition will be discussed Fe and Mn, Ag will give rise toevents excitation theelements Nwith element Mn name evidence of other transitions in coincidence the new to the experiment, RMn-components =events 1.7(2), evidence of other in the sues arethroughout encountered. First all,coincidence both of new thenothan iniron Section 3.2.knowledge Atransitions search ofofparticleshowed Nwith 1% Fe target. With the total ratio of =manganese than 1% eleme 62 62 418-keV transition. the fraction the observed de-excitation intensity the beam, Feofof and Mn, will give toMn excitation of the 418-keV transition. Mn in evidence other transitions in rise coincidence the newmentally to iron throughout the experiment, R = NNwith = 1.7(2), mentall 62 than Fe target associated with Fe be deduced target. With knowledge of can the total ratio [45]: of manganese 418-keV transition. the fraction of the observed de-excitation intensity in thesolution solution N ment Mn = 1.7(2), to iron throughout the experiment, R = Mn inindi↵ere NFe target associated with 621Fe can be deduced [45]: di↵e solut 3the Results and discussion fraction of the observed de-excitation intensity in the ⇣ ⌘ = 0.36(3), FFeand = discussion (5) ditional 3 Results 62 ditiona in di 62 t ( Mn) target associated1 with be deduced [45]: +discussion RMnFe 1tcan the part (62 Fe) 62 ⌘ the par 3 Results and + ⇣ dition F = = 0.36(3), (5) Fe 3.1 21+ state inMn) 62Fe 62 itit isis not 3.1 Excitation Excitation of of the state Fe t ( in no 1 Mn 1the + 2R the 62 62 t ( Fe) 62 face isiscp t ( Fe) + face 1 where and is the ratio of cross sections of exciting 3.1 Excitation of the 2 state in Fe 62 Mn) itelem is 1 ! 1/2  t( F = 0.36(3), (5) trix Contamination of the  5/2 in the 109 Ag Fe = 1 transition 62 Mn) 62 62in the 109 Ag Contamination 5/211target, trix ele 62 σ! t ( 1/2 1 atransition Fe) of1the the state of in the by Fe or Mn beam. face t ( interest + R target that normalisation could only be Mn ratio wheremeant and is the of cross sections of excitingthe targ σ (62 Fe) 62 target meant that could only beperformed performed tare t ( Mn) Contamination ofnormalisation the 5/21 t! 1/2 in the 109 Ag thetrix 1 transition 62 62 the state of interest in the target, by a Fe or Mn beam. target meant that normalisation could only be performed the t

62

Counts per 1 keV

xcitation of

Fe and

62

Mn following in-beam of 62 Mn 5 excitation of L. decay P. Gaffney et al.: Coulomb

500 400 300 200

1200 [keV]

ing the tion on ng and um, alote here mbiguity

in the

(5)

xciting beam. sia [52, 11 keV nent in ! 1/21 erences ctra of s, assotracted tensity

culated ts, and 1 tranition is tion in te from scussed wed no he new

e 109 Ag formed

100 0 300

320

340

360

380

400

420 440 Energy [keV]

Fig. Background-subtracted γ-ray -ray spectra spectra Fig. 7. 6. (Color (Color online) Background-subtracted showing de-excitation. Data Data at atall alltraptrapshowing the the region of the target de-excitation. ping are summed summed in in these thesespectra, spectra, ping and and charge-breeding charge-breeding settings are although the longest longest times. times.The Thespecspecalthough 75% 75% data was taken with the tra detection of of aa projectileprojectiletra are are Doppler Doppler corrected assuming detection like -ray emission from from either either aa projectile-like projectile-like like particle particle and γ-ray (black) (black; or recoil-like The shape particle of the particle black (red) points particle. of Fig. 5) or line recoil-like 311 keV is symmetric expected for the a single γ(red; bluepeak points of Fig. 5). and Theasline shape of 311-keV ray transition fromand the as recoil. The 415 peak-ray clearly shows peak is symmetric expected for akeV single transition contamination, and 415-keV when Doppler corrected for contamination, the projectile, from the recoil. The peak clearly shows a component at 418corrected keV emerges. and when Doppler for the projectile, a component at 418 keV emerges. 62

Fe) and is the ratio of cross sections of exciting where σσtt((62 Mn) the state of interest the ! target, a 62 Fe or 62AMn beam. with respect to the in 3/2 1/21bytransition. complete 1 Calculated using the Coulomb-excitation code, gosia [46, set of E2 and M 1 matrix elements coupling the low-lying − 47], this ratio is 0.9915 for the 3/2 state at 311 keV 109 1 levels of Ag (1/21 , 3/21 , 5/21 ) are defined in the spein 109 Ag. Secondly, there iscode, an additional component in cial version of the gosia gosia2 [52, 53]. Addi− − the Doppler-broadened γ-ray peak of the 5/2 → 1/2 1 1 tionally, known 109matrix elements to the higher-lying states transition in Ag around 415 keV. Using the differences (3/22 , 5/22 ) were included and used as bu↵er states in between peak shape in the Doppler-corrected spectra of the calculation. The gosia2 version of the code allows Figure 6 a second component at 418 keV emerges, assofor a simultaneous least-squares fit of matrix elements in ciated with the projectile. Its intensity can be extracted the target and projectile systems, as well as a common by subtracting the true 5/2− 1/2− intensity 1 → to 1 -transition set of normalisation constants, the observed -ray in− Iγ (5/21 →1/2− 1 ) extracted[37]. fromThe the target ratio, Isystem = 1.13, calculated − − tensities is over-determined by a γ (3/21 →1/21 ) complete set ofpreviously spectroscopic data matrix [54–59]elements, plus theand obin gosia using measured − − served 5/21 intensity ! 1/21 of intensity, therefore provides the “clean” the 311 which keV, 3/2 1 → 1/21 tranthe constraint on the normalisation constant. However, sition. The deduced intensity of the 418 keV transition is + the projectile system is under-determined. almost five times greater than the 2+ → 0 transition in 1 1 62 62 Table 1), meaning that this must originate Fe (see from In Fe, the excitation cross-section of the 2+ 1 is gov62 Mn. The assignment of this transition will be discussed erned in this experiment by only two matrix elements, + + + events showed no in Section 3.2. A search of particle-γ-γ namely h0+ 1 kE2k21 i and h21 kE2k21 i. All other matrix evidence of other transitions in coincidence elements can be shown to influence at thewith leveltheofnew less 418 keV transition. than 1%. However, only one transition intensity is experimentally determined, which means that there is no unique solution to the system. Usually, segmentation of the data 3 Results and discussion in di↵erent ranges of CoM scattering angle provides additional data [37, 50], but because of the ambiguity in 3.1 particle Excitation of the 2+ state in 625) Fe and low statistics, the kinematics Figure 1(see it is not possible in this case. Instead, a total- 2 sur− − 109 Contamination of the transition in the Ag face is created in two5/2 dimensions, each ma1 → 1/21 representing target meant including that normalisation could only be performed trix element, the sum of the contributions from the target and projectile systems and is plotted in Fig-

62

Fe and

62

Mn

5

− with respect to the 3/2− 1 → 1/21 transition. A complete set of E2 and M 1 matrix elements coupling the low-lying − − levels of 109 Ag (1/2− 1 , 3/21 , 5/21 ) are defined in the special version of the gosia code, gosia2 [46, 47]. Additionally, known matrix elements to the higher-lying states − (3/2− 2 , 5/22 ) were included and used as buffer states in the calculation. The gosia2 version of the code allows for a simultaneous least-squares fit of matrix elements in the target and projectile systems, as well as a common set of normalisation constants, to the observed γ-ray intensities [45]. The target system is over-determined by a complete set of spectroscopic data [48–53] plus the ob− served 3/2− 1 → 1/21 intensity, which therefore provides the constraint on the normalisation constant. However, the projectile system is under-determined.

In 62 Fe, the excitation cross-section of the 2+ 1 is governed in this experiment by only two matrix elements, + + + namely h0+ 1 kE2k21 i and h21 kE2k21 i. All other matrix elements can be shown to influence at the level of less than 1%. However, only one transition intensity is experimentally determined, which means that there is no unique solution to the system. Usually, segmentation of the data in different ranges of CoM scattering angle provides additional data [44, 45], but because of the ambiguity in the particle kinematics (see Figure 4) and low statistics, it is not possible in this case. Instead, a total-χ2 surface is created in two dimensions, representing each matrix element, including the sum of the contributions from the target and projectile systems and is plotted in Figure 7(a). Recent lifetime measurements utilising the recoildistance Doppler-shift method, by Ljungvall et al. [26] and Rother et al. [27], provide a further constraint on the totalχ2 surface, represented by the dashed lines in Figure 7(b). In order to treat the uncertainties correctly, both of these lifetime data were included in the gosia2 fit and treated with equal weight to the γ-ray intensities and other data. The resulting 1σ surface is now constrained in both dimensions resulting in an ellipse that represents the correlations between the two parameters. By projecting the point with the minimum χ2 and the limits of this ellipse onto the relevant axis, we are able to extract values and uncertainties of the matrix elements, shown in Table 2. If one were to assume that the spectroscopic quadrupole moment, Qs (2+ 1 ) is zero, or otherwise that the secondorder excitation process can be neglected, a projection can + + + be made to h0+ 1 kE2k21 i at h21 kE2k21 i = 0. The values obtained from this procedure without including the additional lifetime data (i.e projecting Figure 7(a) at x = 0) are also presented in Table 2, although the uncertainties should be considered to be underestimated by neglecting correlations. Consistency between the lifetimes and the current Coulomb-excitation data is however shown. Sensitivity to the sign of Qs is desirable in order to determine the nature and not only the magnitude of deformation. While state-of-the-art shell-model calculations using the LNPS interaction predict a prolate deformation 2 with Qs (2+ 1 ) ≈ −30 efm [20], a relatively simple analysis of Nilsson orbitals with realistic Woods-Saxon potentials predicts an oblate deformation in 62 Fe [54]. Unfortunately,

L. P. P. Ga↵ney Gaffney et et al.: al.:Coulomb Coulombexcitation excitationofof6262 and6262 Mn L. FeFeand Mn

+ h0+ 1 kE2k21 i [efm]

66 60

2

(a)

102

50 40

10 30

+ h0+ 1 kE2k21 i [efm]

20

1

10 45

1.4

(b)

40

1.2

35

1.0

30 0.8 25 0.6

20 -200 -150 -100

-50 0 50 100 + h2+ kE2k2 i [efm] 1 1

150

200

2 Fig. 7. 7. (Color (Color online) online) (a) (a) A two-dimensional totalFig. A full full two-dimensional total-χ2sursur+ + + +i and h2+ +kE2k2+ +i for the 62 face with respect to h2 kE2k0 face with respect to h211 kE2k011 i and h211 kE2k211 i for the 62Fe Fe projectile. (b) (b) The The resulting resulting surface projectile. surface when when combined combined with withthe the lifetime measurements measurements of of Refs. lifetime Refs. [26, [26, 27] 27] and and aa cut cut applied appliedwith with 2 the condition condition that that χ22 < < χ2min +1, representing 11σ. . The individ+1, representing The individthe min ual 1σ 1 contours contours for for the the Coulomb-excitation ual Coulomb-excitation and and lifetime lifetimedata data are shown by the solid and are shown by the solid and dashed dashed lines, lines, respectively. respectively. 62 Table 2. Results in 62 Fe projected from the ellipse obtained Table 2. Results in Fe projected from theofellipse using the full data set, including the lifetimes Refs. obtained [26, 27], + using the full data lifetimes ofusing Refs.only [26, the 27], and projecting theset,22 including surface atthe Qs (2 ) = 0 1+ +1 ) = 0+using only the and projecting the χ surface at Q (2 s Coulomb-excitation data. Note that h01+kE2k21+i and the corCoulomb-excitation data. that h01entirely kE2k21by i and the corresponding B(E2) value areNote constrained the lifetime responding B(E2) value are constrained entirely by the lifetime data. data. with ⌧ (2+ with Qs (2+ 1+) 1 ) = 0 with τ (2 ) with +4 Qs (2+ 1 2 1 ) = 0 + + +1.5 h01 kE2k21 i = 32.0 1.3 efm 31 3 efm2 + +1.5 +4 + 2 h0 kE2k2 ii = 31−3– efm2 +60 efm2 h21+ kE2k21+ = 32.0 10−1.3 efm 1 1 50 + +60 h2+ −10+1.3 efm2 + +i = 12kE2k2 1 −50 W.u. B(E2; 14.0 13+43 –W.u. 1 ! 01 ) = 1.1 + + +1.3 2 B(E2; 21 Q →(2 0 +)) = 14.0 W.u. 13+4 −1.1efm −3– W.u. 8+40 s 1 1 = 40 + +40 2 Qs (21 ) = −8−40 efm –

ever, the sensitivity to Qs (2+ 1 ) can be increased by the variation scattering parameters beam the currentoflevel of uncertainty doessuch not as allow oneenergy, to distarget species or scattering angle. This experiment demontinguish between the two possibilities. In principle how+ strates method and any potentialbynew ever, thethe sensitivity to Qfeasibility increased the s (21 ) canofbe measurements. Higher-beam energies provided HIEvariation of scattering parameters such as beambyenergy, ISOLDE will further increase the This cross-section, increasing target species or scattering angle. experiment demonthe statistical precision. potential for the emergence strates the method and The feasibility of any potential new of shape coexistence in this region [11,provided 55] increases the measurements. Higher-beam energies by HIEinterest in more precision measurements. ISOLDE will further increase the cross-section, increasing the statistical precision. The potential for the emergence

62 of shape coexistence this region [11, 55] the 3.2 Assignment of thein418-keV transition in increases Mn interest in more precision measurements. The identification, in this experiment, of a 418-keV ray transition cannot be reconciled with previous experiments employing -decay [56], multi-nucleon transfer re3.2 Assignment of the 418 keV transition in 62 Mn actions [57], or deep-inelastic reactions [29]. No such transition is observed in these data, although the proposed in in this experiment, of a 418 keV IThe = (6)identification, state, identified both in-beam experiments [29, γray lies transition cannot reconciled with4+previous experi57], 418 keV abovebethe -decaying state. Howments β-decayof[56], multi-nucleon transfer ever, theemploying non-observation the (6) ! (5) 196-keV tran-reactions deep-inelastic No such transition in [57], our or experiment rulesreactions out such[29]. a placement in sition is observedToinunderstand these data,thealthough the level-scheme. origin ofthe thisproposed transition, must identified be knowninif both the ground the isomeric I = (6)it state, in-beamorexperiments [29, state number of experiments 57], is liesCoulomb-excited. 418 keV above Athe β-decaying 4+ state.have Howbeen at ISOLDE of recently us keV to shed ever,performed the non-observation the (6)that → allow (5) 196 tranlight on in thisour question. Firstly, the spins of both -decaying in sition experiment rules out such a placement states were confirmed a laser-spectroscopy the level-scheme. To in understand the origin experiment of this tranatsition, the COLLAPS setup [30, 58]. In this experiment, the it must be known if the ground or the isomeric longer-lived 4+ state (T1/2 =A671(5) ms of [14]) was observed state is Coulomb-excited. number experiments have tobeen haveperformed been extracted with arecently much higher than at ISOLDE that intensity allow us to shed the 1+onstate msthe [56, 59]). a 1/2 = 92(13) light this (T question. Firstly, spins of Secondly, both β-decaying decay of 62 Mn 61] identified an excited 0+ statesexperiment were confirmed in [60, a laser-spectroscopy experiment state that is populated only in the decay of the shorterat the COLLAPS setup [30, 58]. In this experiment, the lived 1+ state, rise1/2to=the 815-keV ray observed longer-lived 4+giving state (T 671(5) ms [14]) was observed intoan earlier have beenexperiment extracted [56]. with a much higher intensity than observed extraction the shorter-lived theCoupling 1+ statethe (T1/2 = 92(13) ms [56,of59]). Secondly, a β+ 1decay stateexperiment in the COLLAPS experiment with theanlong trap-0+ 62 of Mn [60, 61] identified excited ping plus charge-breeding times (in excess of 700 ms for state that is populated only in the β decay of the shorterthe most + significant fraction of the Coulomb-excitation lived 1 state, giving rise to the 815 keV γ ray observed 62 data), is expected that only in an it earlier experiment [56].the long-lived state in Mn persists at the target position in this experiment. A Coupling the observed extraction of the shorter-lived matrix was produced from the sum of all data collected + 1 state in the COLLAPS experiment with the long trapduring the “beam-on” and “beam-o↵” windows throughping plus times (in excess of62700 ms for + out the run.charge-breeding The 0+ Fe, pop2 ! 21 815-keV transition in the most significant fraction of the Coulomb-excitation 62 ulated only in the decay of the low-spin state in Mn [60, data), is expected only the long-lived in 62+Mn 61], wasitnot observedthat in coincidence with thestate 2+ 1 ! 01 persists at the target position in this experiment. A γ-γ 877-keV or in the singles spectra. Upper limits of < 3.2% + all data + matrix was produced from the sum of collected and < 1.8% (2 ) with respect to the 41 ! 21 1299-keV during theare “beam-on” and windows transition determined in “beam-off” the coincidence and62throughsingles + + out the run. The 0 → 2 815 keV transition in that Fe,the pop2 This1 supports our analysis spectra, respectively. 62 ulated only in the+decay of beam the low-spin state in with Mnre[60, content of 62 Mn(1 ) in the was negligible + 61], was nothigher-spin observed state. in coincidence with the 2+ spect to the 1 → 01 877The keVsimplest transition or in theofsingles spectra. Upper limits assumption the origin of the 418-keV + + of < 3.2% and < 1.8% (2σ) with respect to the 4 → -ray is of de-excitation of a state that is excited via 1a sin-21 + 1299 keV transition are determined the coincidence and gle 418-keV E2 transition from the in -decaying 4 state. singles spectra,the respectively. supports By normalising intensity of This this peak usingour the analysis same + that theascontent of 62 Mn(1 )now in the beam method in Equation 5, but with FMnwas = 1negligible FFe , respecttotoextract the higher-spin state. itwith is possible the Coulomb-excitation cross section The and simplest hence a B(E2) value.ofThere are range spin assumption the origin of theof418 keV possibilities for such a state = that 2, 3, 4, 6). However, γ-ray is of de-excitation of a (I state is 5, excited via a sinitgle can418 be keV shown the B(E2)" is relatively4+indeE2that transition from value the β-decaying state. pendent of the assumption of the spin of the finalthe state By normalising the intensity of this peak using same and in allascases results in value ⇡ 30 W.u., method in Equation 5, abut nowofwith FMn = 1more − FFe , + than observed the 2+ it is double possiblethat to extract theforCoulomb-excitation cross in sec1 ! 01 transition 62 Fe. and This hence large aB(E2) value would imply intrinsic tion B(E2) value. There are an range of spin + 2 quadrupole ) ⇡ 122 efm , within rigidpossibilitiesmoment, for suchQ2a(4state (I = 2, 3, 4, 5, 6).theHowever, rotor model [62], which can be compared to the limits it can be shown that the B(E2)↑ value is relatively exindetracted from the assumption spectroscopicofquadrupole meapendent of the the spin ofmoment the final state sured recentresults laser-spectroscopy measurements, and +in inall cases in a value of ≈ 30 W.u., more + +transition is |Q )| < 40that efm2observed [30, 58].for Such 2 (4 double than thea2strong 1 → 01 transition in 62 Fe. This large B(E2) value would imply an intrinsic

L.P. P.Gaffney Ga↵neyetetal.: al.:Coulomb Coulombexcitation excitationofof6262Fe Feand and6262Mn Mn L. Excitation energy of 4(+) isomer, E(4+ ) [keV] 352

350

348

346

344

342

10 9 I (418 keV) [102 ]

2 intensity than the 1+ (T122 = 92(13) msthe [62,rigid66]). 1/2 efm quadrupole moment, Q2state (4+ ) ≈ , within 62 Secondly, a [62], -decay experiment of Mn [32, 67]limits identified rotor model which can be compared to the exan excited state that is populated only moment in the meadecay tracted from0+the spectroscopic quadrupole of the shorter-lived state, giving rise tomeasurements, the 815-keV sured in recent 1+ laser-spectroscopy + 2earlier -decay experiment [62]. ray observed in an |Q (4 )| < 40 efm [30, 58]. Such a strong transition is 2 therefore not expected. In order to reproduce the observed Coupling the observed extraction of the shorter-lived + Coulomb-excitation cross section in the limit of the 1 state in the COLLAPS experiment with the longmeatrapsured quadrupole moment, times the excitation ping plus charge-breeding (in excessenergy of 700 of msthe for state mustsignificant be lower. fraction A scenario similar to “forced isothe most of the Coulomb-excitation mer depopulation” therefore envisaged, such that data), it is expected[63] thatisonly the long-lived state in 62 Mn + the final state of the γ-ray decay is the 1 ground-state persists at the target position in this experiment. Aπ proceeding the excitation an of intermediate I = matrix wasvia produced from theofsum all data collected + + (2 , 3 )the state. In orderand to estimate thewindows positionthroughof this during “beam-on” “beam-o↵” + the β-decaying + new state relative 4+ state, it is62assumed out the run. The 0to Fe, pop2 ! 21 815-keV transition in that they areincoupled by of a the weak E2 transition W.u. ulated only the decay low-spin state inof621Mn [32, + tested+ in strength. The sensitivity to this assumption is 67], was not observed in coincidence with −10 the 21 ! 01 by also taking negligibly small value of 10 and 877-keV or in athe singles spectra. Upper limits W.u. of < 3.2% +the γ-ray aand large value (2 of 5) with W.u..respect It can to bethe shown that < 1.8% 4+ ! 2 1299-keV 1 1 intensity roughly linearly a function of B(E2) transitionfollows are determined in the as coincidence and singles for small values (< 10 W.u.). The energy of the state the is spectra, respectively. This supports our analysis that varied in each 62 case+and the gosia code is used to calcucontent of Mn(1 ) in the beam was negligible with relate γ-ray intensity. For this purpose, it is spectthe to expected the higher-spin state. assumed that there is a 100% branch to the 1+ , following The simplest the origin of the 58,60 the systematics of assumption 2+ states in of Mn [64] and the418-keV energy -ray is of de-excitation of a state that is excited via acan sinfactor in γ-ray decay, and that the electron conversion (+) +4 58,60 gle E2 transition from the -decaying state. By norbe considered negligible. While the 3 states in Mn malising the intensitybranch of thisto peak same method have a non-negligible the using 2+ , it the is expected that as populate in Equation 5, butthat now = 1 and FFethere, it is Mnenergy we the state is with lowestFin possible to branch extract isthe Coulomb-excitation section fore a 100% also assumed for the 3+cross possibility. and results hence aofB(E2) value. There range inof Figure spin posThe such calculations areare plotted 8, sibilities for such a state (I = 2, 3, 4, 5, 6). However, where it is shown that the most likely position of the newit can be the B(E2) " value is4+relatively indestate is ≈shown 72(3) that keV above the β-decaying state, should π of the final itpendent have I πof= the 2+ , assumption or ≈ 77(3) keV for Ispin = 3of+ .the Here, thestate asand in allof cases results in atransition value ofis⇡taken, 30 W.u., more sumption a single-particle such that + + observed than that for W.u.. the 2+ ! 0updated 1 An 1 transition B (E2;double 4+ → (2 , 3+ )) = 1(1) levelin 62 +an +intrinsic Fe. This large B(E2) value would imply scheme showing the placement of the new (2 , 3 ) state + moment, Q2turn, (4(+) )the ⇡ β-decaying 122 efm2 , 4within the isquadrupole shown in Figure 9. In is now +3 + rigid-rotor that can be compared to the limproposed to model lie 346[68] keV above the β-decaying 1 , thus −8 62 its extracted from the of spectroscopic quadrupole moment solving the conundrum which β-decaying state in Mn in state. recent laser spectroscopy measurements, ismeasured the (+) ground |Q2 (4 )| < 40 efm2 [65]. Such a strong transition is therefore not expected. In order to reproduce thetheir observed To interpret these newly-positioned states, enCoulomb-excitation cross section in the limit of the meaergies are compared to similar states in the neighbouring sured quadrupole moment, energy ofMn the isotopes and isotones in Figurethe 10.excitation In both 58 Mn and 60 state are must be lower. A scenario similar “forced isothere a number of positive-parity states to that lie above + merisomeric depopulation” [69] therefore envisaged, that the 4+ state, theisfirst of which are I = 2such states + the54final of the decay is[64]. the 1This ground-state at keVstate and 76 keV, -ray respectively represents via the of anweintermediate I ⇡Mn= aproceeding good candidate forexcitation the state that observe in 62 (+) (+) (2 ,both 3 )its state. In order to estimate the position of this from energy and decay behaviour. An inversion + (+)ruled out, howof thestate the I relative = 2+ and states cannot 4be new to 3the -decaying state, it is asever. Low-lying, positive-parity were alsoof sumed that theylow-spin are coupled by a weak states E2 transition observed Gaudefroy al. [56], fed β decay ofis 1 W.u. inbystrength. Theetsensitivity to in thisthe assumption 62 Cr. With thetaking current placement of the β-decaying 4+ tested by also a negligibly small value of 10 10 W.u. state at anvalue energy 346 keV, ablethat to conclude and large of 5ofW.u.. It canwe be are shown the -ray that the state at 285 keV linearly must have 0. The ofalternaintensity follows roughly as aI = function B(E2) tive scenario of Ref. [56]W.u.). that sees stateof have I = 2is for small values (< 10 The this energy the state would maintain the the isomeric the to 4+calcudue varied not in each case and gosianature code isofused to the potential 59 keV depopulating E2 transition. The late the expected -ray intensity. For this purpose, it is as+ Mn isotopes importance theisνg orbital fortoNthe ≥ 134 sumed that of there a 9/2 100% branch , following the was investigated in shell-model calculations in the pg9/2 systematics of 2(+) states in 58,60 Mn [70] and the fenergy

77

8

340

338

1E-10 1.0 2.0 5.0

W.u. W.u. W.u. W.u.

78

80

336

334

82

84

7 6 5 4 3 2

66

68

70

72

74 +

76 +

E = E(2 , 3 )

+

E(4 ) [keV]

Fig. Fig.8.9. Intensity Intensityofofthe the418 418keV keVγ-ray -raytransition, transition,calculated calculated + inin gosia, gosia,asasaafunction functionofofenergy energydifference di↵erencebetween betweenthe the4 4+ and the newly proposed states, for different values of B(E2) ↑. and the newly proposed states, for di↵erent values of B(E2)+". Filled a a2 2+ Filledsymbols symbolsand andsolid solidlines linesshow showcalculations calculationsassumed assumed + state, state,while whileopen opensymbols symbolsand anddashed dashedlines linesare arefor fora a3 3+state. state. ItItisisassumed for assumedthat thatthe theconversion conversioncoefficient coefficient+ forthe thetransition transition isisnegligible negligibleand andthe thebranching branchingratio ratiototothe the11+ground groundstate stateisis 100%. 100%.The Theexperimentally experimentallydetermined determinedintensity intensityand andassociated associated uncertainty (including uncertainty (includingaacontribution contributionfrom fromthe thenormalisation normalisation 109 109Ag target excitation) are shown by the horizontal toto the the Ag target excitation) are shown by the dashed line dashed line and shaded area, respectively and shaded area, respectively

valence space Theand spin of the the electron ground state is incorfactor in -ray[28]. decay, that conversion can rectly predictednegligible. to be I = While 2+ in all studied, and be considered theisotopes 3+ states in 58,60 Mn the lowest-lying 0+ state in 62 to bethat at have a non-negligible branch toMn the is2+predicted , it is expected 897 keV, more than 600 keV higher than the newly aswe populate the state that is lowest in energy and therefore + (+) signed at 285 keV.assumed The lackforofthe an3isomeric 4+ state a 100%0 branch is also possibility. The inresults these of calculations could point towardsinthe importance such calculations are plotted Figure 9, where ofit πpf shell.that Calculations using position the new of LNPS interacis shown the most likely the new state (+) tion have the Z = 28it is ⇡[20] 72(3) keVshown abovehow the excitations -decaying 4across state, should shell shells (+) key to the evolution of⇡the neutron haveclosure I ⇡ = 2are , or ⇡ 77(3) keV for I = 3(+) . Here, the inassumption this region.ofImportant new experimental developments a single particle transition is taken, such with are driving theoryAn in this dithat COLLAPS B(E2; 4(+)at!ISOLDE 2(+) , 3(+) )= 1(1) W.u.. updated rection [30, 58]. (+) (+) level scheme showing the placement of the new (2 , 3 ) Chiara et al. [29] concluded that the state that lies state is shown in Figure 10. In turn, the -decaying 4(+) 114 keV above the β-decaying 4+ state is the I = 4 mem-+ is now proposed to −1 +1 lie 346 keV above the -decaying 1 , ber of the πf7/2 νg9/2 multiplet. The members of this multhus solving the conundrum of which -decaying state in tiplet would range from 62 Mn is the ground state.1 ≤ I ≤ 8 and have negative parity, the lowestand highest-spin states, members lying To with interpret these newly-positioned their enhigher in energy than the intermediate-spin states, hence ergies are compared to similar states in the neighbouring the reasonand theisotones lowest spins are not observed 60 isotopes in Figure 11. In both 58in Mnthe andyrastMn biased reactions of Refs. [29, 57]. The proposed g neu9/2 there are a number of positive-parity states that lie above tron configuration in the isotones gives to(2 the + yrast the isomeric 4+ state, theFefirst of which is arise I= ) states 9+ state that is observed to decrease in energy with re-a at 54 keV and 76 keV, respectively [70]. This represents 2 62 spect the ground-state configuration within increasing good to candidate for the state that we observe Mn from neutron This behaviour is shown in Figure both itsnumber. energy and decay behaviour. An(−) inversion of 10 the + corresponding + alongside the energies of 4 states from the I = (2 ) and (3 ) states cannot be ruled out, how−1 +1 the proposed πf7/2 νg9/2 multiplet in the Mn isotopes. In ever. Low-lying, low-spin positive-parity states were also the shell-model calculations of [62], Ref. fed [28],inthe observed by Gaudefroy et al. thepresence decayofof 62 negative-parity beginning at of424 in 62 Mn4(+) is Cr. With thestates current placement thekeV -decaying (−) consistent with the current the able 4 to state. state at an energy of 346 placing keV, weofare conclude

8

L. P. Gaffney et al.: Coulomb excitation of (1 )

62 25Mn37

(8-) 541

1500

(7-) (6-)

225

(1 ) 355

(0+)

640

(460)

(2 ,3 )

114

671 ms

(346)

418

285

196 109

(5--) (4 )

(4 )

91 ms

(1 )

Fig. 9. Proposed level scheme of 62 Mn, following the placement of the new (2+ , 3+ ) level at 418(2) keV. The position + of this state is taken to be 72+8 −3 keV above the β-decaying 4 π + state. This reflects the assumption that I = 2 with the possibility that I π = 3+ . In the latter case there would be a 5 keV increase in this energy difference, effectively lowering the energy of the β-decaying 4+ state to 341 keV. Both β-decaying states are shown in red along with their measured halflives [14, 56, 59]. Low-spin states decaying to the β-decaying 1+ state were determined in Ref. [56]. High-spin states decaying to the β-decaying 4+ state were determined in Refs. [29, 57]. The arrows represent experiments, 62 all γ rays 62 that have been observed in previous excitation of Fe andthis Mn following in-beam decay of 62 Mn including work, with their energies labelled in keV.

hat lies I = 4 of this ve negembers states, d in the ed g9/2 e to the gy with reasing gure 11

1600

Mn - E(4+ is )

1400

Mn - E(4( Fe -

1000

)

)

+ E( 92 )

800 600 400 200 0

57

58

59

60

61

62

63

64

65

Fe and

62

Mn

ionisation chamber. From this, we were able to provide an + independent measurement of the B(E2; 2+ 1 → 01 ) value in + 62 Fe under the assumption that Qs (21 ) = 0, previously measured via lifetimes obtained with the recoil-distance Doppler-shift method. Combining the complementary lifetime and Coulomb-excitation data, we were able to perform a first measurement of the spectroscopic quadrupole moment of the first-excited 2+ state, albeit with a large uncertainty. Additionally, a new transition at 418(2) keV has been observed in 62 Mn and is proposed to arise from the decay of a I = (2+ , 3+ ) state, lying just 72+8 −3 keV above the β-decaying 4+ state, to what would be the 1+ ground state. This is the first experimental indication of the relative positions of the 1+ and 4+ states in 62 Mn, crucial for understanding the role of the νg9/2 orbital in shell-model calculations. We acknowledge the support of the ISOLDE Collaboration and technical teams. This work was supported by FWO Vlaanderen GOA/2010/10 (BOF KULeuven), by the IAP Belgian Science Policy (BriX network P6/23 and P7/12), by BMBF under contract 05P12PKFNE, L.P.G. acknowledges support from FWO-Vlaanderen (Belgium) via an FWO Pegasus Marie Curie Fellowship.

References

Mn - E(2+ )

1200 E(I ⇡ ) [keV]

heir enbouring d 60 Mn e above ) states resents n 62 Mn version ed out, es were ecay of ying 4+ onclude alternae I =2 due to The impes was g9/2 vastate is tudied, ulations Calcushown key to ImporAPS at

62

66

67

68

Mass number, A

Fig. 11. 10. Energy Energy systematics systematics of Fig. of selected selected levels levels in in the the Mn Mn isoisotopes around around N N = = 36, topes 36, with with respect respect to to the the ground ground state. state. The The data for for each each isotope isotope is the references: data is taken taken from from the following following references: 58 59 60 61 62 58 Mn [65], 59 Fe [66], 60 Mn [64, 67], 61Fe [68, 69], 62Mn [29, 57, Mn [72], Fe [73], Mn [70, 74], Fe [75, 76], Mn [63, 64, 65 67 and the the present present work], work], 63 63 Fe [69], 65Fe [69], 67Fe [69]. The asand Fe [76], Fe [76], Fe [76]. The as+ sumption of of II = = (2 2 + )isistaken sumption takenhere herefor forthe thenew newstate stateat at 418 418 keV keV 62 in 62 Mn. in Mn.

4 Fe Summary conclusions under theand assumption that Qs (2+ 1 ) = 0, previously measured via lifetimes obtained with the recoil-distance In summary, Coulomb excitation has performed on a Doppler-shift method. Combining thebeen complementary lifemixedand beam of 62 Mn/Fe at REX-ISOLDE. time Coulomb-excitation data, we wereThe ableiron to acomfirst ponent, which of cannot be extracted from the primary ISOL measurement the spectroscopic quadrupole moment of target in conventional means, was produced via the first-excited 2+ state, albeit with a large in-beam uncertainty. the β decay ofathe manganese ThekeV ratiohas of been iron and Additionally, new transitionparent. at 418(2) obmanganese by adjusting trapping and served in 62was Mn controlled and is proposed to arisethe from the decay charge-breeding of the REX-TRAP/EBIS coupling of a I = (2+ , 3+times ) state, lying just 72(3) keV above the before the post-accelerator and would measured in a1+gas-filled -decaying 4(+) state, to what be the ground state. This is the first experimental indication of the relative positions of the 1+ and 4(+) states in 62 Mn, crucial for understanding the role of the ⌫g9/2 orbital in shell-model calculations. 62

We acknowledge the support of the ISOLDE Collaboration and

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