SLAC-PUB-1337 - Stanford University

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of quantum electrodynamics in high Z electronic and muonic atoms is also presented .... in terms of normal Feynman diagrams using bound state or Furry-picture.
SLAC-PUB-1337 (T) November 1973 QUANTUM ELECTRODYNAMICS AND EXOTIC ATOMIC PHENOMENA OF HIGH Z-ELEMENTS

*t

Stanley J. Brodsky Stanford Linear Accelerator Center Stanford University, Stanford, California 94305

ABSTRACT We review the physics of the exotic atomic phenomena, especially positron autoionization,which

can occur if the charge of the nucleus

is increased beyond the critical collision

value Z - 170. The adiabatic

of two heavy ions can be used to study experimentally

the

problem of the Dirac electron in a Coulomb field beyond the critical value where pair production

occurs.

phenomenon are discussed,

including the possible complications

quantum electrodynamic

corrections.

of quantum electrodynamics

Various approaches to this of

A brief review of recent tests

in high Z electronic

and muonic atoms

is also presented.

(Submitted to Comments on Atomic and Molecular

Physics. )

*Work supported by the U. S. Atomic Energy Commission. l-Based on an Invited talk presented to the Seattle meeting of the Division of Nuclear Physics of the American Physical Society, November, 1972.

A fascinating

problem in atomic physics and quantum electrodynamics

the question of what happens physically

is

to a bound electron when the strength

of the Coulomb potential increases beyond Za! = 1. This question involves properties limits

of quantum electrodynamics

of validity

Although

of perturbation

which are presumbably

theory,

a complete field theoretic

so it is an area of fundamental interest.

formulation

of this strong field problem

has not been given, it is easy to understand in a qualitative physically: electron

beyond the

As Za! increases beyond a critical

way what happens

value, the discrete bound

state becomes degenerate in energy with a three-particle

continuum

state (consisting of two bound electrons plus an outgoing positron wave) and a novel type of pair creation occurs. “autoionizing”

Remarkably,

it may be possible that such

positron production processes of strong field quantum

electrodynamics The earliest

can be studied experimentally. discussions of the strong field problem began with the solutions

of the Dirac equation for an electron in a Coulomb field. idealization radiation

since the nucleus is taken as infinitely corrections

V = -Zol/r

are ignored.

heavy and point-like

and

The spectrum of the Dirac equation with

is given by the Dirac-Sommerfield

E= Jxmc2

This is of course an

fine structure

is the binding energy of the 1s state.

formula: Thus E= 0 appears

to be the lower limit of the discrete spectrum as Za! - 1 and E even becomes imaginary

for (Za) > 1. Actually,

this result is just a mathematical

curiosity.

As pointed out by Schiff, Snyder and Weinberg1 in 1940, and also by Pomeranchuk and Smorodinsky,

2

’ 3 a boundary condition is required and by Fermi,

specify the point Coulomb equation.

The solutions are well-defined

nuclear finite size is introduced.

-2-

to completely when any

Thus we should consider the “realistic”

potentials r>R r 0. In order to understand what happens physically the critical

value Zcrit

2 below -mc , we must leave

- 170, where E “dives”

the confines of the single-particle

when Z is increased beyond

Dirac equation.

For the moment we shall

ignore the higher order QED effects from electron self-energy vacuum polarization.

(This can always be done mathematically

sion taking o! small with Za! fixed. ) Clearly, creation

and

- if we envi-

the new phenomena involve pair

since the potential energy in V is sufficient

fact, if we had a state le > = ats 10 > with els = ats al+sb+lO> if e+

erate in energy with the three-particle (the energy of the positron)

corrections

= -els > mc2.

[The positron thus has a normal

energy in the positive continuum. ] The true state of the physical problem is thus a combination of the two types of states

le > and le - e - e+ > . An analogy

with Auger or autoionizing

This state is not discrete,

states is evident. -3-

and

the single particle state.

energy is effectively

The proper description

complex,

corresponding

of the state requires

quantized Fock states of quantum electrodynamics. consistent formulation

of quantum electrodynamics

field theory,

for the strong field problem It is interesting

a state with two 1s bound electrons

is lower in

energy than the state containing no electrons bound to the field. emphasized by Fulcher and Klein, of a Vacuum”

or reference

6

the two particle

state for excitation.

to a strong field with Z greater than Zcrit Peitz, Rafelski,

Zeldovitch, 8 the collision

distribution

to overcome the Coulomb barrier,

Let us suppose that only one ground-state

Then, as the ions collide,

As the ions recede, we are left with two state with an angular

the charge density of the colliding

nuclei.

double pair production with two outgoing continuum positrons if no ground state e- are present. the Pauli principle

electron

the lowest eigenstate becomes mixed

in the 1s level plus an outgoing positronium reflecting

and

a ground state electron sees an effective nuclear

with the le - e - e+ > continuum level. electrons

could be feasible experimentally.

of two heavy ions with ZI+Z2 > Zcrit is considered.

that, at least adiabatically,

is present.

of an electron bound

and Greiner, ‘( and by Gershtein and

The velocity is assumed to be sufficient

potential with R < Rcrit.

Thus as

state is the natural choice

It would be very exciting if the physical realization

In papers by Muller,

and the

Although a complete,

has not yet been given, the essential elements are understood. to note that when Z > Zcrit

to a decaying

Pair production,

if the 1s levels are all full,

Note that

would be possible

however,

so pre-ionization

is suppressed by or stripping

is

necessary. Miiller

--et al.

7

have a given simple estimate for the positron production

rate T+ in the collision

of the two ions (see Fig. 3). The calculations -4-

are only

done to lowest order in Z-Zcrit,

and are similar

his discussion of the autoionization is proportional

problem.

to Z’ = Z1+Z2 -Zcrit

to those made by Fano’ in

The driving potential

6V = V-Vcrit

. Let lsbc> be the single particle

solution

of the Dirac equation go 1+c> E Z.$ II just at the critical particle

+pm+Vcrit

1

I +c> = -mc2 I ec>

value, and let I# E > be the angular momentum zero, three-

continuum state solution of E _< -mc2

re,I~E>=-EI$E>,

.

Then to first order in 6V, E+=mc2+-mc2+~6, I?+ E h/T+ = 27rk~ Clearly,

we require

small R < Rcrit,

6=29 keV - z’ 2y ,

iav lQ12

that the distance R between the two ions be sufficiently

and the collision

overlap time T sufficiently

to r+ in order to satisfy the critical condition. formation

An interesting

10

large compared

field strength condition and the adiabatic

discussion of the experimental

of superheavy quasi-molecules

and Greiner .

y=O.O5 keV

conditions and the

is given by Peitz,

The above estimates are clearly

Miiller,

Rafelski

only a guide: other corrections

of order a! from QED and the presence of the other atomic electrons need to be considered. The observation

of the production

of electron-positron

pairs via the coherent

energy of the nuclear Coulomb field would clearly be a unique physical test of strong field quantum electrodynamics.

However, the physics can be understood

in terms of normal Feynman diagrams using bound state or Furry-picture quantum electrodynamics

(see Fig. 4). We are clearly -5 -

dealing with pair

production

arising from the collision

if the collision

of two charged particles:

times are long enough, the produced e- can bind to one of the nuclei and the outgoing positron will balance the overall linear and angular momentum. the energy to produce the continuum positron the kinetic energy of the colliding atoms.

and bound electron comes from

What is novel here is that the

processes are occurring

in a region where Za! > l, and normal perturbation

theory is inapplicable.

It may also be interesting

which are internally

Clearly

to measure the photons

produced during the collision.

Thus far, the most detailed check of quantum electrodynamics field regime is the comparison between theory and experiment

in the strong

for the K-electron

binding energies in heavy atoms (W, Hg, Pb, Rn) (see Table I) and, most this astonishingly inFermium (see Table II). In particular, 12-17 11 already rules out nonlinear and theoretical work precise experimental dramatically,

modification

of QED of the type suggested by Born and InfeldI’

by two orders

Notice also, that the QED effects due to the electron self-energy

of magnitude.

and vacuum polarization

are being substantially

checked in these comparisons.

The situation is more clouded in the case of muonic atoms of large Z, since there are a few transitions

[especially

the 5g-4f transitions

56 Ba] which show a 20 disagreement

transitions

in

theoretical

calculations

has been given by Kroll.

and experiment. 19

in 82Pb and the 4f-3d

between the most recent

(See Table III. ) A complete review

The current status of Lamb shift measurements

and theory for high Z elements has been reviewed by Erickson. There has been considerable the radiative

corrections

interest

in the question of whether

could modify or even eliminate

cussed here for pair production corrections

theoretical

14

the predictions

dis-

at Z > Zcrit . As we have noted, the radiative

are controlled by a! rather than Za! so they are in principle -6-

independently controllable expect dramatic

in their

and thus one would not

physical effects,

One also would not

changes in the previous description.

expect that calculations

based on a Feynman diagram treatment

indicated by

Fig. 4, could be much affected by effects of order a!. In the case of the self-energy

corrections

to the electron line, a fraction

a! of the lepton charge is spread out over a Compton radius of the electron Ke [ modulo a logarithmic

tail out to the Born radius l/mZol

associated with the

Such a distribution

convoluted with the nuclear size distribution 20 Also, since the determinacould only change Zcrit by a negligible amount.

Bethe sum].

tion of the nuclear radius R derives from electron scattering the influence of radiative

corrections

is already partially

The situation is somewhat more complicated polarization

corrections,

just as small.

experiments,

included.

in the case of the vacuum

although in the end, the modifications

For small r (r