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Register a new userIsospin mixing in a particle-number conserving microscopic approach
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We calculate the isospin-mixing parameter for several Tz=-1, Tz=0 and Tz=1 nuclei from Mg to Sn in the particle-number conserving Higher Tamm-Dancoff approach taking into account the pairing correlations. In particular we investigate the role of the Coulomb interaction and the |Tz|=1 pairing correlations. To do so the HTDA approach is implemented with the SIII Skyrme effective nucleon-nucleon interaction in the mean-field channel and a delta interaction in the pairing channel. We conclude from this investigation that the pairing correlations bring a large contribution to isospin-symmetry breaking, whereas the Coulomb interaction turns out to play a less important role. Moreover we find that the isospin-mixing parameters for Tz=-1 and Tz=1 nuclei are comparable while they are about twice as large for Tz=0 nuclei (between 3% and 6%, including doubly magic nuclei).
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In the present work the so-called Higher Tamm-Dancoff Apporximation method is presented for the generalized case of isovector and isoscalar residual interactions treated simultaneously. The role of different particle-hole excitations and of proton-neutron pairing correlations in the ground state of the self-conjugate 64Ge nucleus is discussed.
We present a number conserving particle-hole RPA theory for collective excitations in the transition from normal to superfluid nuclei. The method derives from an RPA theory developed long ago in quantum chemistry using antisymmetric geminal powers, or equivalently number projected HFB states, as reference states. We show within a minimal model of pairing plus monopole interactions that the number conserving particle-hole RPA excitations evolve smoothly across the superfluid phase transition close to the exact results, contrary to particle-hole RPA in the normal phase and quasiparticle RPA in the superfluid phase that require a change of basis at the broken symmetry point. The new formalism can be applied in a straightforward manner to study particle-hole excitations on top of a number projected HFB state.
The particle-number conserving method based on the cranked shell model is adopted to investigate the possible antimagnetic rotation bands in $^{100}$Pd. The experimental kinematic and dynamic moments of inertia, together with the $B(E2)$ values are reproduced quite well. The occupation probability of each neutron and proton orbital in the observed antimagnetic rotation band is analyzed and its configuration is confirmed. The contribution of each major shell to the total angular momentum alignment with rotational frequency in the lowest-lying positive and negative parity bands is analyzed. The level crossing mechanism of these bands is understood clearly. The possible antimagnetic rotation in the negative parity $alpha=0$ branch is predicted, which sensitively depends on the alignment of the neutron ($1g_{7/2}$, $2d_{5/2}$) pseudo-spin partners. The two-shears-like mechanism for this antimagnetic rotation is investigated by examining the closing of the proton hole angular momentum vector towards the neutron angular momentum vector.
Recently, we have applied for the first time the angular momentum and isospin projected nuclear density functional theory to calculate the isospin-symmetry breaking (ISB) corrections to the superallowed beta-decay. With the calculated set of the ISB corrections we found |V_{ud}|=0.97447(23) for the leading element of the Cabibbo-Kobayashi-Maskawa matrix. This is in nice agreement with both the recent result of Towner and Hardy [Phys. Rev. {bf C77}, 025501 (2008)] and the central value deduced from the neutron decay. In this work we extend our calculations of the ISB corrections covering all superallowed transitions A,I^pi=0^+,T=1,T_z rightarrow A,I^pi=0^+,T=1,T_z+1 with T_z =-1,0 and A ranging from 10 to 74.
Background: The isospin mixing is an interesting feature of atomic nuclei. It plays a crucial role in astrophysical nuclear reactions. However, it is not straightforward for variational nuclear structure models to describe it. Purpose: We propose a tractable method to describe the isospin mixing within a framework of the generator coordinate method and demonstrate its usability. Method: We generate the basis wave functions by applying the Fermi transition operator to the wave functions of isobars. The superposition of these basis wave functions and variationally obtained wave functions quantitatively describes the isospin mixing. Results: Using 14N as an example, we demonstrate that our method reasonably describes both T = 0 and 1 states and their mixing. Energy spectrum and E1 transition strengths are compared with the experimental data to confirm isospin mixing. Conclusion: The proposed method is effective enough to describe isospin mixing and is useful, for example, when we discuss {alpha} capture reactions of N = Z nuclei.
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