European Journal of Scientific Research ISSN 1450-216X / 1450-202X Vol. 144 No 4 April, 2017, pp. 357-381 http://www.europeanjournalofscientificresearch.com
The Quantized Atomic Masses of the Elements: Part-1; Z=1-20; H-Ca Bahjat R. J. Muhyedeen College of Science, Baghdad University, Iraq Email:
[email protected] Abstract This paper is the first part of a series of nine. An innovative semi-empirical atomic mass formulaexcluding binding energy term- has been derived to calculate quantized atomic masses more precisely than macro-micro formula and purely microscopic HF-self-consistent methods. It is based on the novel mass quantization and the variable neutron mass concepts of new nuclear theory NMT. It can calculate the atomic masses of non-existent isotopes based on the existing experimentally measured nuclides with RMS less than 200 keV. The quantized atomic masses of 11000 nuclei ranging from Z=1 to Z=177 have been calculated, 700 nuclides of them belong to Z=1-20; H-Ca in additional to 3500 unquantized mass. The results are compared with those of other recent macroscopic–microscopic. Sn, Sp, β-, β+ and α decay energies are also given. Key word: nuclear mass formula, neutron mass, atomic masses, new isotopes, super-heavy nuclei, alpha decay
1. Introduction A- Background The real estimation for the accurate atomic masses is of great current interest in connection with the present and future experimental studies of nuclei beyond the valley of stability, conducted at the heavyion facilities and the separator DGFRS. The necessity for theoretical calculations of the atomic masses for superheavy nuclides is due to their short half-lives and small cross sections for their synthesis and to discover the Island of Stability. There are two main approaches in the theoretical description of nuclei to evaluate the approximate atomic masses of the isotopes from the proton and neutron number. The first approach is the macroscopic-microscopic approach [1-4]. The macro model could be either liquid drop model or Yukawa-plus-exponential model, or Thomas-Fermi approximation. The micro model could be either Woods-Saxon single-particle potential (universal parameters) or Strutinski shell correction or pairing approximation, BCS. Liquid Drop Model of nuclear binding energy was set up by Weizsäcker [5] in 1935 and also Bethe and Bacher in 1936 [6]. MA=ZMH+NMN -
1
[avA- aa 𝑐2
(N−Z)2 A
- ac
(Z)2 A1/3
- asA2/3 ± aδ A-1]
(1)
The Bethe–Weizsäcker formula was based on the liquid drop model of George Gamow in 1935 and later adapted to a description of nuclear reactions (by Niels Bohr [1936]; and Bohr and Fritz Kalckar [1937]) and to fission (Bohr and John A. Wheeler [1939]; and Yakov Frenkel [1939]). Although several refinements have been made to the parameters of the BE formula over the years [7], the parabolic structure (α+βZ+γZ2) of the formula remains the same till now. Other primitive models such as the nuclear mass systematics that used neural networks, which is mathematical in character [8]. The atomic mass evaluation AME was created by A. H. Wapstra in the 1950’s and following this concept, a series of Mass Tables have been formed over the years, the most recent ones in 1983, 1993, and 2003. WangAudi-Wapstra et al., WAW [9-11] worked on different line where they applied the least square method on experimental atomic masses, atomic binding of Lunney, Pearson and Thibault [12] and nuclear reaction energies for correcting the atomic masses. Muntian et al. [13-15] worked also on the first
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approach where they evaluate the ground state mass of a nucleus (A, Z) using the Yukawa-plus exponential model for the macroscopic part and the Strutinski shell correction for the microscopic part. They considered even–even, odd–odd nuclides and odd-A for nuclei with Z = 82–128 and N = 126–192. Mmacr (Z, N, β0λ ) = ZMH + NMN – av (1 – kvI2)A + as(1 – ksI2)A2/3B1(β0λ ) + a0A0 + c1Z2A-1/3B3(β0λ ) c4Z4/3A-1/3 + f(kFrp)Z2A-1 – ca(N – Z) – aelZ2.39 (2) Möller et al. also used the finite-range droplet macroscopic model FRDM (2012) and the folded-Yukawa single-particle microscopic model to calculate the ground-state masses of 9318 nuclei ranging from 16O to A=339 [16-18]. Three decades later, the second approach appeared in late of 1960s. It is purely microscopic HF-self-consistent methods. The self-consistent methods use calculations of the HartreeFock type with effective density-dependent interactions of the zero-range - Skyrme type- [19, 20] or of the finite-range - Gogny type- [21, 22]. The purely microscopic methods that belongs also the relativistic mean field approach [23–25] intensively used in recent years in the description of nuclear properties. Although the nuclear shell theory succeeded in explanations of some nuclear effects but still it cannot help in predicting the stability of SHE. The failure of macro-microscopic models in prediction of atomic mass of non-existent isotopes is due to the lack of real understanding of the nuclear structure. The macro focus on the whole component while the micro focus on the individuals. The results of both models give inaccurate atomic masses due to routine treatment on the mass formula parameters. Consequently, the accurate estimation of the atomic masses of the existent and non-existent isotopes is considered as unsolved problem. The output of most theoretical calculations cannot predict the atomic masses precisely which lead to improper alpha energies and half-lives. The atomic masses calculated by WAW et al. [11] and Moller et al. [18] failed to give the positive incremental difference in alpha energies between two sequential isotopes as we will see later. An immense project was setup in 2010 to solve this problem. As a nuclear and quantum chemist, I understand that there is no specific model and wave function that can describe the nuclear system perfectly. In HF-SCF, each wave function may succeed in estimation of one or few nuclear properties such as atomic mass, binding energies, fission barrier, energy decay, self-fission, cross section etc. In a similar manner, in quantum chemistry we have more than fifty wave functions to describe the molecular system and each wave function may describe few molecular properties such as geometry, HOMOLUMO, ionization potential, IR, UV, NMR spectra and so on. Therefore, in present project a new semiempirical strategy is setup to adopt the measured atomic masses inserting them into special quadratic equations and then extrapolate them to predict the accurate atomic masses for the non-existent element’ isotopes. In this manner, NMT is avoiding any theoretical treatment which lead to inaccuracy in the prediction processes. The new ansatz depends on the pure nuclear property i.e. atomic masses of the nuclei and avoids the external corrections used in the two main approaches in the theoretical description of nuclei. This article is part I of an immense project started in 2010. The aim of the project is to find out 1- a quantized mass formula QMF to the elements that have enough isotopes to setup a polynomial equation based on the available isotope masses (i.e. Z=1-110), it will be called isotopic quantized mass formula IQMF, 2- two quantized mass formula QMF to the elements that do not have enough isotopes (i.e. Z=111-118) to setup a polynomial equation that will create atomic masses for non-existent isotopes, they will be called analytical and numerical quantized mass formula AQMF and NQMF, and to generate a database for alpha energies for more than 1140 isotopes for Z=100-118, and 3- a quantized mass formula QMF to the non-existent elements that will create atomic masses for more than 4000 new non-existent isotopes, from the alpha energies database, it will be called energetic quantized mass formula EQMF (i.e. Period-8, Z=119-172 and period-9, Z=172-177). In present year, the whole project is accomplished successfully. The polynomial equation of the 2nd power generates the quantized atomic masses QAM while the polynomial equation of 3rd up to 6th power generates the unquantized atomic masses UQAM. Both QAM and UQAM of the elements Z=1-118 have been calculated. The QAM of the isotopes of the Period-8 & 9 Z=119-177 have been calculated. The accuracy of UQAM is 327 keV.
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B- Theory The standard model theory SMT essential concepts of the mass formula are based on the theory that both masses of protons and neutrons are invariant inside and outside of the nuclei and the energy has a mass, therefore, the atomic masses of the nuclei can be estimated from subtraction of the binding energy (which has a mass; fictitious mass) from the mass number A (i.e. MA=ZMH+NMN-B.E-Be(Z)). In this article, the mass quantization and the mass-energy conformity concepts of the new theory are applied, which is termed the Nuclear Magneton Theory of Mass Quantization, or NMT [26-28]. The NMT concepts, regarding the atomic masses, are different from SMT concepts where NMT supposes that the mass of the proton is invariant inside and outside of the nuclei while the mass of the neutron Mn∗ is variable inside the nuclei and the mass of the nucleon could not be converted to energy or vice versa to create the binding energy. But still both SMT and NMT follow the quantum mechanical system. The atomic masses MA of the nuclei can be estimated from summation of the total mass of the protons and electrons or MH and total mass of the variable neutron masses Mn∗ (i.e. MA=ZMH+NMn∗ ) avoiding B.E concept. The NMT model is considered as a modified SMT model. NMT shows the reason for the nucleon decay but SMT shows which mode it will follow. Application of the mass quantization concept on the neutron mass Mn∗ inside the nuclei helps in calculating the atomic masses MA of existent and non-existent isotopes which gives excellent results far from using any external parameter correction to the B.E. terms. The mass quantization concept is a part of NMT theory which is founded on the concept of quantized elementary discrete mass particles (the socalled electron neutrinos), herein called the Magneton and Antimagneton. The particles are conceived to be spinning magnetic dipoles with sufficient mass to produce the dipole-dipole interaction sufficient to act at ultra-short range - the source of the Nuclear Force Field (NFF) - which now has a gravitational component. Since the NFF contains this component it can be thought of as the long searched for Unified Field. The NMT believes that the numbers of the basic building blocks are only two, the magneton and its antimagneton rather than twelve (6-quarks, 6-Leptons). These basic building blocks arranged in circular closed quantized packages rings as nmtionic shells to form the fermions. Both the electron and the proton have three negative and positive charge nmtionic K, L and M shells, while the neutron has four nmtionic K, L, M and N shells where the 1st K and 4th are negative and 2nd L and 3rd M are positive. The variety of the different spin-rotation direction of the magnetons of the four shells of the neutron lead to a tiny negative charge, electric dipole moment and a negative value of magnetic moment. The negative charge of the 4th shell of the neutron reduces the Coulomb repulsion which mightily support the shell structure model in description the stability of the ultraheavy nuclei with Z>140. This novel structure of the neutron find the solution to the unsolved problem of the negative value of its magnetic moment. The mass quantization concept means that any particle has a certain number of the building blocks and its stability is controlled by four criteria [28]. In 2008, NMT considers all other heavier neutrinos as a multiple package of electron neutrino (i.e. magnetons). In 2012, Xing Zhi-Zhong reported a remarkable indication of the νμ → νe oscillation which is consistent with a relatively large value of θ13 in the three-flavor neutrino mixing scheme [29]. Another related discovery was on July 19, 2013, at the European Physical Society meeting in Stockholm, where the international T2K collaboration announced a definitive observation of muon neutrino to electron neutrino transformation [30]. On the other hand, on February 2014, K. Abe et al. conducted an experiment at T2K and they observed electron neutrino appearance in a muon neutrino beam produced 295 km from the Super-Kamiokande detector with a peak energy of 0.6 GeV [31]. In 2014, Volpe and Balantekin [32] explored the state of the art and current issues surrounding nucleosynthesis, as well as the part neutrinos have to play in this cosmic game of creation, a confirmation of the fact that electron neutrinos are fundamental building blocks of matter. Finally, the Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2015 to Takaaki Kajita (SuperKamiokande Collaboration University of Tokyo, Kashiwa, Japan) and Arthur B. McDonald (Sudbury
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Neutrino Observatory Collaboration Queen's University, Kingston, Canada) for the discovery of neutrino oscillations, which shows that neutrinos have mass [33]. The results of above studies support NMT concepts. Thus, the matter quantization series starts from molecules, atoms, fermions and finally the magnetons. The basic building block magneton quantizes the mass, charge, nuclear energy, half-life and radioactivity [28].
2. Method The general procedures and policies of calculation of the quantized atomic masses QAM
2.1 Application of Mass Quantization Principle on the Neutron NMT believes that; contrary to the mass of the electron QMe and the proton QMp which they have a fixed quantized mass inside and outside the atom, the neutron has several variable masses Mn∗ in the stable nuclei which are called quantized QNM and in the unstable poor and rich nuclei which are called unquantized UQNM/UQNM as explained below: Definition-1: Variable Neutron Masses Mn∗ NMT denotes Mn∗ to the variable neutron masses in the nuclei to differentiate it from the wellknown fixed free neutron mass MN outside the nuclei with mass equal to 1.00866491588 u. The values of Mn∗ inside the nucleus will be represented by; 1-QNM (blue color) to refer to quantized neutron mass in stable nuclides, 2-UQNM (green color) to the unquantized neutron mass in unstable neutron-poor NP nuclides and 3-UQNM (red color) to the unquantized neutron mass in unstable neutron-rich NR nuclides. NMT uses these colors to help the reader to identify the type of the neutron mass. The value of variable neutron mass Mn∗ is simply calculated from subtraction of the total proton and electron mass i.e. ZMH from the atomic masses MA and divided by the total neutron number N as seen in the following formula; Mn∗ = (MA-ZMH)/N
(3)
For example, the QNM value in the stable isotope 40Ca is equal to = (39.962590864 - 20MH)/N =0.990304511 u, and UQNM in the unstable neutron poor NP isotope 39Ca is equal to = (38.970710813 - 20MH)/N = 0.990221587810526 u and UQNM in the unstable neutron rich NR isotope 47Ca is equal to = (46.95454243-20MH)/N =0.992520066125926 u. Definition-2: Neutron Mass Plateau If we imagine that the quantized mass QNM of the stable isotope of any element located in the middle of the neutron mass stability curve (plateau), then the values of unquantized mass of the neutrons UQNM and UQNM in the isotopes series will be distributed up UQNM and down UQNM of the plateau (above +∆ and down -∆). The radioisotope which is closer (small |∆| in neutron mass) to the plateau will have a longer half-life with lower energy (β-, β+ or α) while the farther radioisotope (large |∆| in neutron mass) from the plateau will have a shorter half-life with higher energy as shown in Fig. 1 based on the Mass Quantization Principle MQP. Usually the number of packages of magnetons of the neutron in neutron-rich nuclei UQNM are greater than the quantized packages of magnetons of the neutron in stable nuclei i.e. UQNM>QNM while they are less in the neutron neutron-poor nuclei i.e. UQNM41 can follow the linear equation with R2≥0.99. While Pearson correlation coefficient R reflects the extent of a linear relationship between Mn∗ and ln(A), R2 value can be interpreted as the proportion of the variance in Mn∗ attributable to the variance in ln(A) in the NMQE. Definition-4: CNM and DNM NMT sorts out the Mn∗ values and nominates the Mn∗ values based on their R2 values formed by the NMQE as dissonant neutron mass DNM (i.e. DNM, DNM and DNM) if they give Mn∗ -ln(A) graph with poor R2 values ((R20.9999) to give NMQE that lead to provision of GNM. The correction of DNM and CNM values to GNM values is achieved through modifying them to give the neutron mass quadratic equation NMQE with higher R2 exceed 0.9999 that achieve the following criteria as shown in Scheme -1. The main criteria that bound the calculated GNM are; i- the even and odd curves of each element inside the graph have to show the parallelism with gap. Usually, inside the graph, the gap between isotopes of small A is larger than that in large A. The gap increase with increasing Z. This gap deforms the parallelism in the element of Z>130 and convert it to twisting in higher Z, ii- the even curve should be lower than odd curve in even Z but vice versa for odd Z, iii- the calculated GNM should give harmonization curves of the sequential elements, iv- the GNM values have to generate quantized atomic masses QAM that give the proper sequential values for β-, β+, 𝑄𝛼𝑇ℎ energies without deviation and discontinuities, v- the calculated QAM should lead to the positive incremental difference in alpha energies between two sequential even-even and odd-odd mass number A; which denoted by the term ∆α (ee,oo). The ∆α (ee,oo) values (i.e. violet values in the Tables 1-20 in the appendix-1) should be positive if the atomic masses are quantized. Otherwise, the atomic masses are not quantized. The second term is also considered during conversion CNM to GNM that the differences between each two sequential α-energy values of even-A
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Bahjat R. J. Muhyedeen
and odd-A or vice versa ∆α (eo,oe) has to be positive incremental values (i.e. blue values in the Tables 1-20), vi- the calculated QAM values have to be very close to the existing values, vii- the calculated QAM values should give the proper β- and β+ values in the element Z+1 and Z-1 respectively and proper 𝑄𝛼𝑇ℎ energies values in Z and be suitable for α-decay energies in the next element Z+2. Normally, NMT avoids the modification of the quantized neutron mass QNM of the stable and relatively stable nuclides. Achieving these criteria is a very challenging job because they conflict each other, consequently, this work requires 5 years of continuous work where more than 11000 isotopes are treated. The variable neutron mass values are functions of Z, N, A, Eb/A, masses, half-lives, decay energies, magic numbers, deformations, shapes, sizes, shell structure and other properties of the nucleus. Therefore, NMT coins them as “Nucleus Master Key”. The Mass Quantization Principle MQP believes that the variable neutron masses inside the nucleus have to increase regularly with a fixed number of magneton packages in the nucleus with increasing the neutron number N. The regular increment in the neutron masses should create the DNM or CNM in different nuclides with increasing Z and N.
Scheme -1: Flowchart to show the conversion DNM or CNM to GNM
That means there is a systemic increment in the neutron mass starting from neutron poor to neutron rich. NMT refers to the fixed increment in the neutron masses due to N increment as quantization process. The fixed increment in neutron masses in the isotopes of the element results in giving the positive incremental values in ∆α (ee,oo) and ∆α (eo,oe). Furthermore, the NMT entitled the isotopic quadratic equations as Isotopic Quantized Mass Formula IQMF (Eq. 5) for the same reason and the atomic masses generated from GNM as quantized atomic masses QAM due to the quantization process. Fig. 8A shows how the IAEA values of DNM of neutron poor have higher values than the DNM of the neutron rich which give arbitrary β-, β+, 𝑄𝛼𝑇ℎ energies for the element with Z=1-20. Fig. 8B shows the corresponding NMT treated consonant and hermetic GNM variable neutron masses values. NMT checked the neutron masses of more than 3430 isotopes of the elements Z=1-118 of IAEA {and also JAEA (Audi et al., Private Communication (April 2011))} and found out that all of them are dissonant and non-hermitic neutron mass DNM (i.e. DNM, DNM and DNM) except seven elements; Z=92-99 (of 99 elements) show a consonant neutron masses CNM. They do not give sequential α energies. For example, the DNM, DNM and DNM of the isotopes of Z=33-72 and Z=79-92 displayed deviation in the parabolic curves that result in discontinuities in 𝑄𝛼𝑇ℎ energies.
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A- The IAEA dissonant neutron masses DNM of light B- The corresponding NMT generalized neutron masses elements; Z=1-20 isotopes. GNM of light elements; Z=1-20 isotopes. Figure-8: A-The dissonant neutron masses from IAEA and B- The generalized neutron masses of light elements’ isotopes after correction; Z=1-20.
A- The dissonant neutron masses DNM of the isotopes B- The corresponding generalized neutron masses GNM of the elements; Z=81-99 of IAEA. values of the isotopes of the elements; Z=81-99 of NMT. Figure-9: The dissonant neutron masses of isotopes of the elements Z=81-99 of IAEA. The circle in Figure-A shows the deviation (curvature) of the IAEA neutron mass values which give discontinuities in 𝑄𝛼𝑇ℎ energies for their isotopes. FigureB shows the corresponding generalized neutron masses GNM of NMT.
Fig. 9A shows the deviation (curvature, marked by a circle) of the IAEA neutron mass values which give discontinuities in 𝑄𝛼𝑇ℎ energies for their isotopes. Fig. 9B shows the generalized neutron masses of isotopes of the elements Z=81-99. Table-2 lists the discontinuities in 𝑄𝛼𝑇ℎ energies and marked by red color for the elements Z=86-93. The incorrect values of 𝑄𝛼𝑇ℎ energies due to the dissonant and nonhermetic neutron masses span from neutron poor to neutron rich passing the plateau of the stable isotopes. The discontinuities in 𝑄𝛼𝑇ℎ energies of IAEA lead to a curling curve of Eα vs N as seen in Fig. 24 in Appendix-1.
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Table-2: The incorrect 𝑄𝛼𝑇ℎ energies of some isotopes of element Z=86-93 from IAEA Neptunium Z=93, A=219-249
Uranium Z=92, A=219249
8983.22 10086.13 10350.25 9909.45 9634.24 9232.79 8786.56 8197.89 7816.46 7308.55 7014.08 6778.14 6368.44 6011.97 5625.80 5357.01 5194.03 5006.58 4958.54 4691.22 4607.19 4558.92 4309.47 4099.65 4114.20 3974.77 3834.75
8428.70 8774.78 9940.13 10209.93 9836.68 9429.96 8940.96 8619.88 8014.65 7701.01 7211.36 6803.08 6475.21 5992.77 5576.31 5413.66 4908.59 4857.70 4678.22 4572.92 4233.52 4269.77 4131.41 4036.28 3817.05 3569.92 3369.00
Protactinium Z=91, A=219-249 8429.45 8393.95 8270.95 8241.70 8097.05 8488.84 9815.06 10084.66 9648.72 9247.76 8885.68 8326.33 7693.73 7392.55 6986.85 6580.44 6264.58 5834.91 5439.41 5149.99 4626.70 4366.95 4077.09 4092.77 3754.64 3794.69 3627.96 3555.30 3154.75
Thorium Z=90, A=219249 8202.00 8273.09 8068.96 7942.95 7958.01 7839.05 7827.15 7664.67 8072.41 9435.34 9848.82 9514.16 8953.09 8625.78 8127.00 7566.68 7298.54 6921.44 6450.90 6146.64 5520.12 5167.59 4769.79 4213.24 4081.63 3760.24 3673.25 3376.37 3333.35 3207.85 3307.80 3307.80 2977.77
Actinium Z=89, A=219249 7944.53 7844.95 7726.88 7729.26 7607.25 7621.69 7518.87 7499.35 7352.17 7745.92 9235.43 9831.59 9377.46 8826.56 8347.86 7783.65 7137.41 6783.24 6326.94 5935.12 5535.85 5042.22 4676.40 4452.52 3872.94 3652.17 3360.45 3208.78 2905.72 2867.85 2811.96 2819.41
Radium Z=88, A=219249
Francium Z=87, A=219249
Radon Z=86, A=219249
7896.64 7741.85 7636.61 7486.45 7415.23 7273.30 7273.10 7143.08 7150.84 7041.87 7031.68 6861.89 7272.82 8864.22 9525.75 9160.75 8545.97 8137.90 7592.43 6880.44 6678.86 5979.03 5788.88 5096.80 4870.70 4365.05 4072.03 3589.47 3344.22 2905.76 2828.59 2535.05 2420.73 2325.72
7812.30 7622.59 7521.07 7389.35 7274.85 7170.49 7054.68 6923.44 6893.32 6784.75 6777.42 6671.61 6662.22 6528.97 6904.81 8588.60 9540.39 9174.27 8469.24 8014.00 7448.58 6800.78 6457.80 5825.80 5561.90 4994.47 4613.19 4162.64 3832.89 3233.16 2854.81 2471.36 2156.19 1876.74 1785.45
8040.05 7862.39 7694.15 7616.71 7410.72 7349.35 7136.29 7043.33 6860.72 6773.77 6629.83 6546.47 6386.16 6383.86 6251.17 6260.70 6155.51 6158.95 5965.40 6385.03 8242.82 9208.46 8839.07 8197.41 7887.14 7262.58 6946.16 6404.71 6162.42 5590.30 5283.23 4756.93 4335.50 3836.04 3382.41 2908.30 2407.02 2074.21 1748.19
The correction process for these neutron masses values will affect the values of the atomic masses of these isotopes of IAEA, therefore, NMT avoids a complete correction for Z=81-83 only to keep the difference between IAEA atomic masses of stable nuclides and NMT atomic masses as minimum as possible. 2.2 The General Procedure for the Calculation of the Quantized Atomic Masses 1- Collecting the atomic masses and other properties values of the isotopes from IAEA, JAEA, WangAudi-Wapstra (WAW) [11], and from Moller et al [18] for element Z=1-118. 2- Deriving the variable neutron mass Mn∗ from the above atomic masses (see Definition-1). 3- Using the polynomial functions to link Mn∗ with ln(A) to setup the NMQE and the isotopic quantized mass formula IQMF for the element Z=1-107 (see Definitions-2-6) to calculate the QAM. 4- Calculating the 𝑄𝛼𝑇ℎ energies of the isotopes for the element Z=1 to Z=99 consecutively.
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5- Moving back from Z=99 to Z=1 sequentially to calculate the positive ∆α (ee,oo) values. The aim of this step is to depend on to 𝑄𝛼𝑇ℎ energies of the appropriate alpha emitter element Z=84-99 6- Moving again from Z=1 to Z=99 to calculate the positive ∆α (eo,oe) values. 7- Deriving and using the analytical quantized mass formula AQMF and the numerical quantized mass formula NQMF to create the atomic masses for 270 isotopes belong to the element Z=108-118 as these elements don’t have enough isotopes (4 RP for even and 4RP for odd) to setup polynomial equation. Each isotope can be created from its four ancestors. The 𝑄𝛼𝑇ℎ energies of the 270 isotopes have been calculated. 8- The 𝑄𝛼𝑇ℎ energies of additional 1140 isotopes were also calculated belong to the elements Z=100118 with positive values for ∆α (ee,oo) and ∆α (eo,oe) and used to setup the database for the 4400 isotopes belong to the element Z=119-172 of Period-8 and 400 isotopes belong Z=173-177. 9- Deriving and using the energetic quantized mass formula EQMF, which derive the neutron masses Mn from the daughter to the mother keeping the positive values of ∆α (ee,oo) and ∆α (eo,oe) to secure the quantization of the atomic masses QAM. EQMF succeeded in calculation of the quantized atomic masses QAM for Z=119-172. The results of items 7, 8 and 9 will be published in the next articles. 2.3 The Special Isotopic Quantized Mass Formula for the Existent Elements Z118. For example, Muntian et al. [15] calculated the 𝑄𝛼𝑇ℎ energies for 119 starting from A=291 up to 307, the values of Alpha for nuclides with A=291-297 are 12.89, 12.73, 12.62, 12.38, 12.55, 12.65, and 12.86 MeV respectively. It is very clear that they decreased to the minimum at 12.38 then increased up to 12.86 MeV.
Figure-11: Comparison of the neutron masses among IAEA, Moller-FRLDM and present work NMT
Figure-12: Comparison of the RMS of UQAM and QAM with others. UQAM RMS=187 keV
Summary The variable neutron mass and their corresponding GNM are calculated for 750 isotopes belong to Z=1-20 as explained in the definitions 1-6 and Scheme-1. The calculated QAM from GNM values result in the positive difference in 𝑄𝛼𝑇ℎ energies between two sequential even-even and odd-odd mass number A (i.e. ∆α (ee,oo)) and even-odd and odd-even mass number A (i.e. ∆α (eo,oe)). The calculated QAM values finally give the proper sequential values for β-, β+, α-decay energies without deviation and discontinuities as seen in Table-4. The QAM of the non-existent isotopes can be calculated by substitution of their mass number A into the NMQE (Mn= α*ln(A)2 - β*ln(A)+ γ) and then into isotopic quantized mass formula IQMF; QAM= ZMH + N(α*ln(A)2 - β*ln(A)+ γ). Only the quantized atomic
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Bahjat R. J. Muhyedeen
masses QAM can give the positive values for ∆α (ee,oo) and ∆α (eo,oe) which should be started from Z=1 up to Z=99. These positive values have been calculated for more than 7000 isotopes belong to Z=1118 in addition to 3500 UQAM. With help from these positive values, NMT succeeded in calculation of the QAM of more than 4400 isotopes belong to period 8, Z=119-172, and Z=173-177 of period-9 that they will be submitted in the subsequent articles. NMT also succeeded in finding out the Island of the Stability. In the present article we discussed the QAM of the isotopes of the first twenty elements Z=120. The UQAM are very close to the IAEA. Moller FRLDM values are closer to IAEA while FRDM values are closer to QAM than IAEA. 3. Results and Discussion The Quantized and Unquantized Atomic Masses (QAM and UQAM)-NMT- 2015 version 3, of Z=1-20 Figures and Tables are in the Appendix-1. The polynomial equations of the 2nd power were used to generate the quantized atomic masses QAM. The mass formula has RMS 1.09 MeV for quantized atomic masses QAM at stable nuclei and 6.01 MeV at far neutron poor and rich. Actually, the values of RMS of QAM does not reflect the accuracy of the calculated QAM values rather than show the discrepancies with IAEA values. The polynomial equations of the 3rd up to 6th power were used to generate the unquantized atomic masses UQAM with RMS of 0.23 MeV. The UQAM of the elements Z=1-20 have been calculated and listed in Table-21. The UQAM are very close to the IAEA. The NMT values of the proton Sp and neutron Sn separation energies are plotted in the Figures 21-24. The NMT QAM give a smooth curve for 𝑄𝛼𝑇ℎ vs N while IAEA and WAW’ Eα show curling curves (see Fig. 25-27). The smooth and straight curves of 𝑄𝛼𝑇ℎ confirm the mass quantization concept. The UQAM, Moller and IAEA failed to give the positive values for the two terms ∆α (ee,oo) and ∆α (eo,oe). The QAM values are compared with IAEA, JAEA, WAW and Moller (FRDM) as seen in Table-21. 1- Hydrogen The hydrogen element has three even isotopes and three odd from IAEA in addition to odd isotope 7H from WAW. The two isotopes 1H and 2H cannot be used as reference points RP as they do not fall in the field of the polynomial of Neutron Mass Quadratic Equation NMQE (see Fig. 1A). NMT generated the GNM after several modifications to the DNM (see Fig. 1B). Table-1 shows the difference between beta energies of IAEA and NMT. NMT added 12 new isotopes 7H - 18H to the literature. The RMS in calculation of the QAM is 6.02 MeV for all isotopes and 3.75 MeV for 2D stable nuclide. The RMS in calculation of the UQAM is 3.23x10-11 MeV for all isotopes. 2- Helium The helium element has 4 even isotopes and 4 odd isotope from IAEA 2He - 10He. The 8 isotopes were used as reference points RP in NMQE (see Fig. 2A). The polynomial of even isotopes gives higher R2 value than the odd isotopes, and both give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 2B). Table-2 shows the difference between beta energies of IAEA and NMT. It shows also that atomic mass of 3He is overestimated. NMT added 11 new isotopes 11He - 21He to the literature. The RMS in calculation of the QAM is 4.5 MeV for all isotopes and 6.37 MeV for stable nuclides; 3He and 4He. The RMS in calculation of the UQAM is 1.1x10-9 MeV for all isotopes. 3- Lithium The lithium element has 5 even isotopes and 5 odd isotope from IAEA 4Li - 13Li. The 10 isotopes were used as reference points RP in the NMQE, 12Li & 13Li from WAW (see Fig. 3A). The RP 4Li value is overestimated and shows high deviation in the polynomial of even isotopes. The RP 5Li value is underestimated and shows high deviation in the polynomial of odd isotopes, and both curves give DNM.
The Quantized Atomic Masses of the Elements: Part-1; Z=1-20
18
NMT generated the GNM after several modifications to the DNM (see Fig. 3B). Table-3 shows the difference between beta energies of IAEA and NMT. NMT added 13 new isotopes 3Li, 12Li - 23Li to the literature. The RMS in calculation of the QAM is 3.31 MeV for all isotopes and 1.12 MeV for stable nuclides; 6Li and 7Li. The RMS in calculation of the UQAM is 3.87x10-8 MeV for all isotopes. 4- Beryllium The beryllium element has 6 even isotopes and 6 odd isotope from IAEA 4Be -13Be. The 12 isotopes were used as reference points RP in the NMQE (see Fig. 4A). The RP 8Be and 9Be value showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 4B). Table-4 shows the difference between beta energies of IAEA and NMT. The isotope 8Be shows a negative energies for β-, β+, α and seems to be formed only in nuclear transparency where the fusion reactions are in equilibrium state, see page 588 in ref [26] and thus 8Be does not stand alone or emit alpha but disintegrated into eight nucleons and become stable when another 4 nucleons fused to form 12C. NMT added 9 new isotopes 17Be - 25Be to the literature. The RMS in calculation of the QAM is 5.76 MeV for all isotopes and 0.073 MeV for stable nuclide 9Be. The RMS in calculation of the UQAM is 3.88x10-6 MeV for all isotopes. 5- Boron The boron element has 5 even isotopes and 5 odd isotope from IAEA 8B - 17Be. The 12 isotopes were used as reference points RP in the NMQE (see Fig. 5A). The RP 8B - 11B value showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 5B). Table-5 shows the difference between beta energies of IAEA and NMT. NMT added 15 new isotopes 6B, 18B - 31B to the literature. The RMS in calculation of the QAM is 3.95 MeV for all isotopes and 1.76 MeV for stable nuclides; 10B and11B. The RMS in calculation of the UQAM is 46.85x10-7 MeV for all isotopes. 6- Carbon The carbon element has 8 even isotopes and 5 odd isotope from IAEA. The 13 isotopes were used as reference points RP in the NMQE (see Fig. 6A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 6B). Table-6 shows the difference between beta energies of IAEA and NMT. NMT added 14 new isotopes 7C, 19C, 23C - 33C to the literature. The RMS in calculation of the QAM is 6.60 MeV for all isotopes and 2.81 MeV for stable nuclides; 12C and 13C. The RMS in calculation of the UQAM is 4.99x10-5 MeV for all isotopes. 7- Nitrogen The nitrogen element has 8 even isotopes and 7 odd isotope from IAEA. The 15 isotopes were used as reference points RP in the NMQE (see Fig. 7A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 7B). Table-7 shows the difference between beta energies of IAEA and NMT. NMT added 13 new isotopes 8N, 9N, 25N - 35N to the literature. The atomic masses of 8N - 11N are UQAM. The RMS in calculation of the QAM is 5.81 MeV for all isotopes and 4.05 MeV for stable nuclides; 14N and 15N. The RMS in calculation of the UQAM is 3.82x10-2 MeV for all isotopes. 8- Oxygen The oxygen element has 8 even isotopes and 7 odd isotope from IAEA. The 15 isotopes were used as reference points RP in the NMQE (see Fig. 8A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 8B). Table-8 shows the difference between beta energies of IAEA and NMT. NMT added 15 new isotopes 10O, 11O, 27O - 39O to the literature. The atomic masses of 10O -
19
Bahjat R. J. Muhyedeen
14
O are UQAM. The RMS in calculation of the QAM is 5.57 MeV for all isotopes and 2.76 MeV for stable nuclides; 16O-18O. The RMS in calculation of the UQAM is 2.73x10-6 MeV for all isotopes. 9- Fluorine The fluorine element has 9 even isotopes and 9 odd isotope from IAEA. The 18 isotopes were used as reference points RP in the NMQE (see Fig. 9A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 9B). Table-9 shows the difference between beta energies of IAEA and NMT. NMT added 14 new isotopes 10F - 13F, 32F - 41F to the literature. The atomic masses of 10F 14 F are UQAM. The RMS in calculation of the QAM is 4.62 MeV for all isotopes and 0.07 MeV for stable nuclide 19F. The RMS in calculation of the UQAM is 0.21 MeV for all isotopes. 10- Neon The fluorine element has 10 even isotopes and 9 odd isotope from IAEA. The 19 isotopes were used as reference points RP in the NMQE (see Fig. 10A). Most of RP values showed high deviation in the polynomial of even and odd isotopes, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 10B). Table-10 shows the difference between beta energies of IAEA and NMT. NMT added 15 new isotopes 12Ne - 15Ne, 35Ne - 45Ne to the literature. The atomic masses of 12 Ne - 18Ne are UQAM. The RMS in calculation of the QAM is 4.81 MeV for all isotopes and 0.85 MeV for stable nuclides; 20Ne - 22Ne. The RMS in calculation of the UQAM is 0.28 MeV for all isotopes. 11- Sodium The sodium element has 10 even isotopes and 10 odd isotope from IAEA. The 20 isotopes were used as reference points RP in the NMQE (see Fig. 11A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 18Na - 21Na, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 11B). Table-11 shows the difference between beta energies of IAEA and NMT. NMT added 18 new isotopes 12Na - 17Na, 38Na - 49Na to the Literature. The atomic masses of 12Na - 19Na are UQAM. The RMS in calculation of the QAM is 4.81 MeV for all isotopes and 0.85 MeV for stable nuclides. The RMS in calculation of the UQAM is 0.283 MeV for all isotopes. The RMS in calculation of the QAM is 5.65 MeV for all isotopes and 0.44 MeV for stable nuclide 23Na. The RMS in calculation of the UQAM is 0.22 MeV for all isotopes. 12- Magnesium The magnesium element has 11 even isotopes and 11 odd isotope from IAEA. The 22 isotopes were used as reference points RP in the NMQE (see Fig. 12A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 19Mg - 25Mg, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 12B). Table-12 shows the difference between beta energies of IAEA and NMT. NMT added 16 new isotopes 14Mg - 18Mg, 41 Mg - 51Mg to the literature. The atomic masses of 14Mg - 21Mg are UQAM. The RMS in calculation of the QAM is 7.31 MeV for all isotopes and 0.93 MeV for stable nuclides; 24Mg - 26Mg. The RMS in calculation of the UQAM is 0.33 MeV for all isotopes. 13- Aluminum The aluminum element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 13A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 21Al - 24Al, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 13B). Table-13 shows the difference between beta energies of IAEA and NMT. NMT added 17 new isotopes 14Al - 20Al, 44Al -
The Quantized Atomic Masses of the Elements: Part-1; Z=1-20
20
53
Al to the literature. The atomic masses of 14Al - 23Al are UQAM. The RMS in calculation of the QAM is 7.12 MeV for all isotopes and 0.05 MeV for stable nuclide 27Al. The RMS in calculation of the UQAM is 0.098 MeV for all isotopes. 14- Silicon The silicon element has 12 even isotopes and 11 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 14A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 22Si - 25Si, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 14B). Table-14 shows the difference between beta energies of IAEA and NMT. NMT added 17 new isotopes 16Si - 21Si, 45Si - 55Si to the literature. The atomic masses of 16Si - 25Si are UQAM. The RMS in calculation of the QAM is 9.23 MeV for all isotopes and 0.42 MeV for stable nuclides; 28Si - 30Si. The RMS in calculation of the UQAM is 0.44 MeV for all isotopes. 15- Phosphorus The phosphorus element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 15A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 25P - 30P, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 15B). Table-15 shows the difference between beta energies of IAEA and NMT. NMT added 20 new isotopes 16P - 24P, 47P - 57P to the literature. The atomic masses of 16P - 27P are UQAM. The RMS in calculation of the QAM is 7.07 MeV for all isotopes and 0.11 MeV for stable nuclide 31P. The RMS in calculation of the UQAM is 0.35 MeV for all isotopes. 16- Sulfur The sulfur element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 16A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 27S - 32S, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 16B). Table-16 shows the difference between beta energies of IAEA and NMT. NMT added 21 new isotopes 18S - 26S, 47S, 49S 59 S to the literature. The atomic masses of 18S - 30S are UQAM. The RMS in calculation of the QAM is 6.63 MeV for all isotopes and 0.81 MeV for stable nuclides; 32S-34S, 36S. The RMS in calculation of the UQAM is 0.33 MeV for all isotopes. 17- Chlorine The chlorine element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 17A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 29Cl - 32Cl, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 17B). Table-17 shows the difference between beta energies of IAEA and NMT. NMT added 19 new isotopes 20Cl - 27Cl, 52Cl - 61Cl to the literature. The atomic masses of 20Cl - 32Cl are UQAM. The RMS in calculation of the QAM is 6.22 MeV for all isotopes and 0.29 MeV for stable nuclide; 35Cl and 37Cl. The RMS in calculation of the UQAM is 0.35 MeV for all isotopes. 18- Argon The chlorine element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 18A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 31Ar - 34Ar, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 18B). Table-18 shows the difference between beta energies of IAEA and NMT. NMT added 19 new isotopes 22Ar - 30Ar, 54Ar 63 Ar to the literature. The atomic masses of 22Ar - 33Ar are UQAM. The RMS in calculation of the QAM
21 is 5.94 MeV for all isotopes and 1.13 MeV for stable nuclides; 36Ar, calculation of the UQAM is 0.36 MeV for all isotopes.
Bahjat R. J. Muhyedeen 38
Ar and
40
Ar. The RMS in
19- Potassium The potassium element has 12 even isotopes and 12 odd isotope from IAEA. The 24 isotopes were used as reference points RP in the NMQE (see Fig. 19A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 33K - 36K, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 19B). Table-19 shows the difference between beta energies of IAEA and NMT. NMT added 20 new isotopes 24K - 32K, 57K - 67K to the literature. The atomic masses of 24K - 36K are UQAM. The RMS in calculation of the QAM is 6.10 MeV for all isotopes and 0.63 MeV for stable nuclides; 39K and 41K. The RMS in calculation of the UQAM is 0.46 MeV for all isotopes. 20- Calcium The calcium element has 11 even isotopes and 12 odd isotope from IAEA. The 23 isotopes were used as reference points RP in the NMQE (see Fig. 20A). Most of RP values showed high deviation in the polynomial of even and odd isotopes especially the light isotopes 34Ca - 37Ca, and both curves give DNM. NMT generated the GNM after several modifications to the DNM (see Fig. 20B). Table-20 shows the difference between beta energies of IAEA and NMT. NMT added 21 new isotopes 24Ca - 33Ca, 59Ca 69 Ca to the literature. The atomic masses of 24Ca - 36Ca are UQAM. The RMS in calculation of the QAM is 8.05 MeV for all isotopes and 1.41 MeV for stable nuclides; 40Ca, 42Ca - 44Ca and 46Ca. The RMS in calculation of the UQAM is 0.55 MeV for all isotopes. 4. Conclusion The NMT theory believes that the mass of the proton is invariant inside and outside of the nuclei while the mass of the neutron Mn∗ is variable inside the nuclei and the mass of the nucleon could not be converted to energy or vice versa to create the binding energy. The special characteristic property of the variable neutron mass Mn∗ is that it can have several neutron masses QNM, UQNM and UQNM inside the nuclides of the same element. NMT sorts out the Mn∗ values and nominates the Mn∗ values based on their R2 values formed by the neutron mass quadratic equation NMQE {Mn= α*ln(A)2 - β*ln(A)+ γ} as dissonant neutron mass DNM if they give Mn∗ -ln(A) graph with poor R2 values ((R2
