Phonon coupling effects in magnetic moments of magic and semimagic nuclei

Abstract

Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semimagic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by Fayans et al. The perturbation theory in g 2 L is used where gL is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g 2 L accuracy. An approximate method is suggested to take into account higher order terms in g 2 L . Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of −(0.1 ÷ 0.5) µN and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratios g ph L of all low-lying phonons in 208 Pb. For the 3 − 1 state it is rather close to the Bohr-Mottelson model prediction whereas for other L-phonons, two 5 − and six positive parity states, the difference from the Bohr-Mottelson values is significant.

Spectroscopic factors of magic and semimagic nuclei within the self-consistent theory of finite Fermi systems

“…The cases of preference of each limit value are divided approximately in half. As in [8][9][10], the PC Z-factor in Just as in calculations of the PC contributions to the single-particle spectra [9], the contribution of the 3 − phonon as a rule dominates. However, sometimes the total contribution of other phonons is comparable to the one of 3 − .…”

“…Below, we It should be stressed that our calculations do not contain any new parameters. The set DF3-a parameters [12] of the Fayans functional proved to be rather successful in describing various nuclear characteristics including nuclear charge radii [20], the excitation energies and BE2 values for 2 + 1 states in lead and tin isotopes [16], the quadrupole moments of odd nuclei [21], PC corrections to magnetic moments [8,10], and single-particle levels of magic nuclei [9]. As to the parameter λ 02 governing the value of Z 0 in nuclear matter, it was found in [7] from the analysis of single-particle spectra in magic nuclei.…”

“…Here we deal with the perturbation theory in δΣ operator with respect to the quasiparticle Hamiltonian H 0 . As well as in [8][9][10], we use the so-called g 2 L -approximation which is, as a rule, applicable to magic nuclei. Here g L is the L-phonon creation amplitude.…”

“…In this case, simple formulas for PC corrections to nuclear characteristics in systems without pairing [8][9][10] can be used. In practice, we found proton and neutron SFs in magic 40,48 Ca and 208 Pb nuclei and proton ones in semimagic lead isotopes.…”

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

“…Extraction of the spectroscopic factors from the reaction 1) e-mail: Sapershtein EE@nrcki.ru data is a complicated theoretical problem, therefore the list of known spectroscopic factors is rather limited. However, the PC corrections to the SPEs are necessary not only by themselves, they are also usually important ingredients of the procedure of finding PC corrections to other nuclear characteristics, e.g., magnetic moments and M 1 transitions in odd nuclei [7,8,9]. PC corrections to the double odd-even mass differences found in the approach starting from the free N N potential [10,11] is another example where the PC corrections to SPEs are of primary importance.…”