Gamow-Teller β⁺ decay properties of A=98 isobars near ¹⁰⁰Sn doubly magic core

Nuclei in doubly magic regions near drip lines have been subject of both theoretical and experimental studies that aim to well understand the spectroscopic behaviour of nuclear forces in such regions. Therefore, the heaviest N=Z magic core ¹⁰⁰Sn situated in the proton drip line and near the rp-process provides important information on nuclear structure and astrophysics [1,2].

The first excited states of ⁹⁸Cd were first identified by Gorska et al. (1997). They have proposed its experimental level scheme and associated $j^{\pi }$ =8⁺to the T_1/2=0.48 µs isomer [3]. In 2004, Blazhev et al. [4] have observed a core excited 12⁺ isomer and measured T_1/2=0.23 µs and 0.17 µs in ⁹⁸Cd. Huyse et al. (1978) discovered the ⁹⁸Cd $\beta$ ⁺ daughterwith the LISOL facility, following the irradiation of ⁹²Mo with a 110 MeV ¹⁴N [5]. The ⁹⁸Ag $\beta$ ⁺ descendent was identified and reported by AtenJr and Vries-Hamerling (1955) [6].

Brown and Rykaczewski (1994) theoretically studied GT $\beta$ ⁺ decay properties of nuclei near ¹⁰⁰Sn mass region [1]. They have presented their spectroscopic calculations using SNB interaction [1] in fpg space model, for odd-even and odd-odd nuclei in near ¹⁰⁰Sn. Covelo et al. (2006) have performed shell model calculations for nuclei in the vicinity of ¹⁰⁰Sn core using an interaction derived from CD-Bonn one in gdsh space model [7]. They obtained good agreement with the experimental data.

In this paper, we have studied the $\beta$ ⁺ Gamow-Teller decay properties of A=98 proton rich isobars near the doubly magic tin-100 core by means of shell model calculations using Oxbash nuclear structure code [8].

The shell evolution is the result of the interactions between the magic core, and the adding nucleons [9,10,11] or the so-called monopole effect described byPoves and Zuker [12] and defined in terms of the two-body interaction. Hence, the consideration of this effect can reproduce the missing nuclear properties of nuclei far from stability. They proposed to express the monopole Hamiltonian of the system in terms°: [13,14,15],

sand/or t denote a proton and/or a neutron orbit. n _{s, t} and T _{s, t} refers, respectively, to the number and the isospin operator defined by A. P. Zuker (2003) [9,14] as a function of the monopole Hamiltonian diagonal part $V_{st}^{\tau \tau \text{'}}$ [11], and $\tau$ ( ${\tau }^{\prime }$ ) stands for proton or neutron.

In this work, we have used the recent single particle energies (SPEs), and considered the mass and the monopole effects to introduce some modifications on the two body matrix elements (TBMEs) of the original interaction jj45apn from ⁷⁸ Ni mass region (Jensen [16,17]). These TBMEs are used in order to calculate the monopole terms:

$V_{1g_{\frac{9}{2}}2d_{{}_{\frac{5}{2}}}}^{pn}\approx -430keV,V_{1g_{\frac{9}{2}}1g_{\frac{9}{2}}}^{pp}\approx 112keV\text{and}{V}_{2d_{{}_{\frac{5}{2}}}2d_{{}_{\frac{5}{2}}}}^{nn}\approx -18keV$ tomodify TBMEs chosen basing on the energetic sequence of the single particle space. Using the resulting interaction jj45m and the original one, some calculations are carried out in order to reproduce the nuclear and $\beta$ ⁺ Gamow-Teller transition propertiesof A=98 isobars.

The $\beta$ decay rate, ${\lambda }_{ij}$ , of transition from the state i to the state j, and the allowed (ft) _ij values can be estimated using [18]:

f _ij denotes the $\beta$ decay phase space factor. (ft)^{GT, F} are the (ft) values for Gamow-Teller (GT) and Fermi (F) transitions, which can be expressed in terms of the matrix elements M_GT and M_Fused to estimate the GT and F transition probabilities [19],

In this work, we have performed shell model calculations, using the new interaction jj45m in $\pi$ (0f _5/2 , 1p _3/2 , 1p _1/2 and 0g _9/2 ) ^Z-28 and v (0g _7/2 , 1d _5/2 , 1d _3/2 ,2s _1/2 and 1h _11/2 ) ^N-50 model space using ¹⁰⁰ Sn as a magic core. The experimental single hole and single particle energies taken, respectively, from ⁹⁹ In for protons and ¹⁰¹ Sn for neutrons are used as a starting point to calculate the effective single particle energies [20,21] using in the interaction.

The calculated configuration changes between the initial and final states indicate that the important values are observed for $\pi$ g_9/2 and vg_7/2. Which means that the ⁹⁸Cd and ⁹⁸Ag protons in the $\pi$ g_9/2 populate the ⁹⁸Ag and ⁹⁸Pd neutrons in vg_7/2 respectively.

Most of the strength of the ⁹⁸Cd→⁹⁸Ag GT transition, limited by a Q_EC value of 5.43 MeV, is located in two peaks concentrated at about 1.5 MeV and 4.5 MeV.For the ⁹⁸Ag→⁹⁸Pd GT transition, limited by a Q_EC value of 8.25 MeV, it is located in two peaks concentrated at about 2.5 MeV and 4.5 MeV.

This study is based on the energetic spectra and Gamow-Teller properties calculations, for odd- odd A=98 isobars, with few hole protons and neutrons in their valence spaces. The calculations are realized in the framework of the nuclear shell model, by means of Oxbash nuclear structure code. Using the jj45apn original interaction of the code, we carried out some modifications based on the proton-neutron monopole interaction to get jj45m interaction. The calculated energetic spectra are in agreement with the experimental data for ⁹⁸Cd and ⁹⁸Pd;however, the spin and parity of ⁹⁸Ag ground state are not reproduced. The ⁹⁸Cd and ⁹⁸Ag protons in the $\pi$ g_9/2 populate the ⁹⁸Ag and ⁹⁸Pd in vg_7/2 respectively.

The obtained half lives of the studied transitions have the magnitude of the experimental ones. The studied GT transitions are limited by Q_EC values of 5.43 MeV and 8.25 MeV. Most of the strength of the ⁹⁸Cd →⁹⁸Ag GT transition is located in two peaks concentrated at about 1.5 MeV and 4.5 MeV. Most of the strength of the ⁹⁸Ag →⁹⁸Pd GT transition is located in two peaks concentrated at about 2.5 MeV and 4.5 MeV.