Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.Comment: 10 pages, 3 figures, 4 tables. Revised for re-submission to Phys. Rev.

Time-dependent Dirac equation applied to one-proton radioactive emission

Relativistic energy-density functional (REDF) theory has been developed and utilized for self-consistent meanfield calculations of atomic nuclei. The proton-emitting radioactivity can provide a suitable reference to improve the predicting ability of REDF especially on the proton-drip line. One needs to consider the quantum tunneling effect, which plays an essential role in nucleon-emitting radioactive processes. However, the relativistic quantum tunneling has been less investigated compared with the non-relativistic case. This work is devoted to a theoretical evaluation of one-proton ($1p$) radioactivity based on the relativistic Dirac formalism. For this purpose, I develop the time-dependent (TD) Dirac-spinor calculation to simulate the $1p$ emission. By utilizing the relativistic Hartree-Bogoliubov (RHB) calculation with the DD-PCX parameters, single-proton potentials for the time-dependent Dirac spinor are determined. The TD-Dirac calculation is applied to the $1p$ emissions from the $^{37}$Sc and $^{39}$Sc nuclei, which can be well approximated as the valence proton and the proton-close-shell cores. The sensitivity of $1p$-emission energy and decaying width to the mass number is demonstrated. Remarkable sensitivity exists due to the size of system, which affects the nuclear part of potentials and energy levels, whereas the Coulomb barrier is common with the same atomic number. The calculated $1p$ energy and decaying lifetime are roughly consistent to the experimental limitation. The present TD-Dirac calculation is expected as applicable widely to proton-rich nuclides in order to improve the REDF by utilizing the $1p$-emission data.Comment: 11 pages, 10 figures, 3 table

Instruction of my personal computing library

This document is prepared to introduce and explain how to use the computing library composed by T. Oishi. The library-01 TOSPEM solves, for the spherical nucleus, (i) the Schroedinger equation for the single-nucleon states within the Woods-Saxon potential, (ii-a) the electric or magnetic transition strength, B(EJ) or B(MJ), between the arbitrary set of initial and final states of the nucleus of interest, and (ii-b) Weisskopf estimate for comparison with results in (ii-a). The library-02 RESONA is composed to solve the resonant eigenstates of spherical Schroedinger equations. The final version is expected to be published for educational and commercial purposes. Before the official publication, under the agreement with publishers, I make the current, preliminary version open for public. Two applications, GFORTRAN and GNUPLOT, are necessary for full usage. Feedbacks and comments on products will be appreciated. The source codes etc. are available in the GitHub repository [1].Comment: arXiv admin note: text overlap with arXiv:2303.1052

陽子過剰な原子核の陽子対相関と二陽子放出崩壊

要約のみTohoku University萩野浩一課

Discerning nuclear pairing properties from magnetic dipole excitation

Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of $S_{12}=0$ with $L_{12}=0$ (spin-singlet s-wave) and $S_{12}=1$ with $L_{12}=1$ (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (RNEDF). The pairing correlations are taken into account by the relativistic Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic quasi-particle random-phase approximation (RQRPA) is employed to describe M1 transitions. We have shown that M1 excitation properties display a sensitivity on the pairing model involved in the calculations. The systematic evaluation of M1 transitions together with the accurate experimental data enables us to discern the pairing properties in finite nuclei.Comment: 5 pages, 6 figure

Triplet-odd pairing in finite nuclear systems (I): Even-even singly-closed nuclei

Background: The appearance of the pairing condensate is an essential feature of many-fermion systems. There are two possible types of pairing: spin-singlet and spin-triplet. However, an open question remains as to whether the spin-triplet pairing condensate emerges in finite nuclei. Purpose: The aim of this work is to examine the coexistence of the spin-singlet and spin-triplet like-particle pairing condensates in nuclei. We also discuss the dependence on the type of pairing functional. Method: The Hartree-Fock-Bogoliubov calculations with a Skyrme $+$ local-pair energy-density functional (EDF) are performed to investigate the pairing condensate in the spherical ground states of Ca and Sn isotopes. Results: The spin-singlet pair EDF induces not only the spin-singlet but also the spin-triplet pairing condensates due to a strong spin-orbit splitting. By discarding the spin-orbit EDF, only the spin-singlet pairing condensate appears. The spin-triplet pair EDF, however, induces the spin-orbit splitting and accordingly the spin-singlet pairing condensate. Conclusions: The spin-orbit splitting plays an essential role in the coexistence of the spin-singlet and spin-triplet pairing condensates in nuclei.Comment: 8 pages, 4 figure