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0POSSIBILITY OF OBSERVING PARITY NONCONSERVATION
Abstract. The space parity-violation effects that occur in the atomic x-ray spectra of Mo, W, Au, and U in the presence of electron-nuclear weak currents are considered. The quantities characterizing the degree of parity violation are of the order of ~ 10-7. Partial estimates of the experimental possibilities of detecting the effect are considered.
Keywords: neutral weak current, space parity, asymmetry, forbidden transition, magnate and electrical dipol transition, neutral bosons.
Introduction
Weak neutral current interactions are one of the ways in which subatomic particles can interact by means of the weak force. These interactions are mediated by the neutral Z- W0 boson. The discovery of weak neutral currents was a significant step toward the unification of electromagnetism and the weak force into the electroweak force, and led to the discovery of the W and Z bosons.
Exchange of a Z boson transfers momentum, spin, and energy, but leaves the interacting particles' quantum numbers unaffected - charge, flavor, baryon number, lepton number, etc. Because there is no transfer of electrical charge involved, exchange of Z particles is referred to as "neutral" in the phrase "neutral current". However, the word "current" here has nothing to do with electricity - it simply refers to the exchange of the Z particle.
Neutral atoms are easily available objects for investigation. Calculations of parity-violation effects can be performed for the inner shells of atoms with a sufficient degree of accuracy. This makes it possible, in the case of experimental detection of parity-violation effects, to reach unambiguous conclusions about the magnitude and sign of the constant for neutral weak currents
Formulation of the problem and main results
Parity violation in decays of atoms and ions can be detected from the appearance of circular polarization of the radiation or from the asymmetry in the emission of photons and photoelectrons with respect to the direction of the initial polarization of the atom. [8-9]. The degree of parity violation is defined by the expression
where < V > is the matrix element of the effective weak interaction operator, which mixes states of opposite parity, AE is the energy interval between these states (we assume that, effectively, only two states are mixed), W0 is the probability of the basic transition with neglect of the weak interaction, and W is the probability of the transition from the level hybridized by the weak interaction.
The effective potential of the electron-nuclear weak interaction for the atom or ion has the form (in units with h =c=1)
IN X-RAY SPECTRA OF HEAVY ATOMS
Melibayev M.
Associate Professor of Kokand State Pedagogical Institute https://doi.org/10.5281/zenodo.14010730
[1-8].
(1)
Ven=-^z(g? • y(e) + g2na(n)) 5(r) (2)
where n is the number of electrons in the atom, 7s(e), a^(e) are Dirac matrices acting on the electron wave functions, c(n) is the spin of the nucleus, G is the Fermi weak-interaction constant, g™ and
g2n are certain constants, depending on the number of protons (Z) and neutrons (N) in the nucleus. In the Weinberg model
g (Z, N) = Z (1 - (N+Z) / 2Z - 2Sin20w) (3)
where 6W is a free parameter? The constant gfn depends on the angular-momentum coupling in the nucleus. From the data of the latest neutrino experiments Sin26w = 0.25. [8,11].
It follows from (1) that we must look for cases in which levels of opposite parity are close together and must use the forbidden transitions from these levels to lower-lying levels. We have ascertained the relative positions of the energy levels from the data of [12]. In the Table we give the value of AE for some of the most favorable situations. For the basic transition we have selected the magnetic-dipole M1 transition K- L, where K (1s1/2) and L (2 Sy2) are respectively the initial
and final hole states. The level nearest to L, with the opposite parity is Ln (2_p1/2)
The amplitude of the one-quantum transition with allowance for the weak interaction is depicted in Figs. a and b. On mixing of the levels L and (2_p1/2) by the weak interaction, owing
to the interference of the amplitudes of the basic (a) and E1 - electrical dipole hybrid (b) transitions, the final photons acquire circular polarization.
Fig. 1. Feynman graphs corresponding to the basic transition and hybrid transition in the ion.
TABLE 1
Element AE a.u. W , ^ W , ^ |P|
Mo W Au U 7.10 20.60 23.95 31.53 3.02 • 1010 1.33 • 1013 2.75 • 1013 1,55 • 1013 1.471015 1.65 1016 2.18 1016 4.16 • 1016 1.49- 10-5 0.64- 10-7 0.83 10-7 2.24 • 10-7
Here, i is 2s, f - 1s, and j is 2p. Z- W0 is the intermediate boson and N is the nucleon.
The probability of emission of a photon with polarization e in the direction n is equal to W(n,e)= W0 (1+P(nS)), (4)
where S =-i[e*X e] is the photon spin. For the transition probabilities W0 =W(K — L ) and W1
(K-L ) we have used the data of the relativistic calculations of [12,13]. The values of W0 , and
W for the transitions that we are considering are given in the Table 1 [13].
The results were checked by analytic calculations with Coulomb wave functions, which should give the correct results for S for one-electron ions and the inner shells of heavy atoms.
The high intensity of the basic 4 transition (W0 ) for large values of Z should be noted,
and is an important advantage of the experiments on heavy atoms.
The details of the calculation of the matrix elements of the weak interaction (2) between the relativistic wave functions are given in [9,10]. Using the same methods of calculation for the matrix elements <V>, we can obtain the following final expression
G
< n'j'I'm' |V| njlm>=- - j= gi (Z, N) (5)
4W 2
X{Ro(nj'l';njl)-Ro(njf;njl) }Sa ,
where
Ro(n'j'l') n/T)= lim gn< j,l,(r)fnjl(r), here, gn' ¡'liand fnji(r) are the upper and lower radial components of the Dirac wave function; njlm are the single electron quantum numbers. A bar above the letter l implies the replacement l ^2j- l, and a bar above njl imlies replacement of gn< ¡'li by fnji(r).
In the calculation of the limit in (5) it is necessary to take into account the finite size of the nucleus. For the radial functions g and f we have used the Dirac self-consistent field functions obtained with the aid of the RAINE program. [14].
This program takes the finite size of the nucleus into account. The results of the calculations are given in the Table. The high intensity of the basic transition (W0 ) for large values
of Z should be noted, and is an important advantage of the experiments on heavy atoms. Conclusion
Let us estimate the measurement time necessary for observation of the effect. To determine the degree of parity nonconservation P in a transition with partial probability B it is necessary to record N~ B-1 P 1 events.
If we use an ion beam with density p traveling with velocity v in a volume V with a cross section S and length l, the number of decays N of the level in time t in this volume is
N= pvSt[ 1- exp(-l/v zp ) ] ,
where , t is the total lifetime of the level Z^ (2p1/2). As a result we obtain the following expression for the time of observation t:
t= t /V pB P2
where
t =l/v [1 - exp(-l/v tp ) ]-1= l/v ( Tp <<l/v) or Tp (tp » l/v)
In the case of experiments with ion we have v~ 108 cm/sec, p~ cm3105 cm-3, and for our transition we find t ~ l/v.
If we assume B ~ 10-5 this gives t ~ (107 / V [ cm3 ]) sec. Hence it follows that to obtain an acceptable observation time t ~ 103 sec it is necessary to use a volume V~ 104 cm3
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