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On-line version ISSN 2075-5635

Nucleus  no.63 Ciudad de La Habana Jan.-June 2018


Nuclear Sciences

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

Propiedades de la desintegración β+ de Gamow-Teller de isóbaros con A = 98 cercanos al núcleo 100Sn doblemente mágico

Nadjet LAOUET1  *  , Fatima BENRACHI1 

1Frères Mentouri Constantine 1 University, PhysicsDepartment, Constantine-ALGERIA


In this work, we have realized some spectroscopic calculations in the framework of the nuclear shell model, in order to estimate the Gamow-teller (GT) β +decay of A=98 proton rich isobars in 100Sn mass region near rp-process path. The calculations are carried out by means of Oxbash nuclear structure code, taking into account the monopole effect in the studied mass region. The obtained results are then compared to the available experimental data.

Key words: nuclear structure; strontium 100; monopoles; o codes; gamow-teller rules; beta-plus decay


En este trabajo hemos realizado algunos cálculos espectroscópicos en el marco de trabajo del modelo nuclear de capas para estimar la desintegración β + de Gamow-Teller (GT) de isóbaros ricos en protones con A = 98 en la región de masa 100Sn, cerca del camino del proceso rp. Los cálculos se llevan a cabo mediante el código de estructura nuclear de Oxbash, teniendo en cuenta el efecto monopolo en la región de masa estudiada. Los resultados obtenidos se comparan luego con los datos experimentales disponibles.

Palabras-clave: estructura nuclear; estroncio 100; monopolos; códigos O; reglas de GAMOW-TELLER; desintegración beta positiva


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 jπ =8+to the T1/2=0.48 µs isomer [3]. In 2004, Blazhev et al. [4] have observed a core excited 12+ isomer and measured T1/2=0.23 µs and 0.17 µs in 98Cd. Huyse et al. (1978) discovered the 98Cd β + daughterwith the LISOL facility, following the irradiation of 92Mo with a 110 MeV 14N [5]. The 98Ag β + descendent was identified and reported by AtenJr and Vries-Hamerling (1955) [6].

Brown and Rykaczewski (1994) theoretically studied GT β + 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 β + 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 Vstττ' [11], and τ ( τ ) 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:

 V1g922d52pn430 keV, V1g921g92pp112 keVandV2d522d52nn18 keV 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 β + Gamow-Teller transition propertiesof A=98 isobars.

The β decay rate, λij , 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 β 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 MGT and MFused to estimate the GT and F transition probabilities [19],




In this work, we have performed shell model calculations, using the new interaction jj45m in π (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.

Figure 1 Calculated spectra with jj45pm interaction in comparison with the experimental ones (left) and β+ decay (right) of A=98 isobars. 

The calculated configuration changes between the initial and final states indicate that the important values are observed for π g9/2 and vg7/2. Which means that the 98Cd and 98Ag protons in the π g9/2 populate the 98Ag and 98Pd neutrons in vg7/2 respectively.

Figure 2 Calculated B(GT) (bars) and Σ B(GT) (vertical steps) of A=98 isobars as a function of excitation energy. 

Table 1 Experimental and calculated T1/2 for 98Cd and 98Ag 

T1/2Exp(s) T1/2Cal(s) Qβ+(MeV) ∑B(GT)
98Cd 9.2 98.920 4.410 14,566
98Ag 47.5 2.61 7.23 1,337

Most of the strength of the 98Cd→98Ag GT transition, limited by a QEC 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 QEC 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 π g9/2 populate the 98Ag and 98Pd in vg7/2 respectively.

The obtained half lives of the studied transitions have the magnitude of the experimental ones. The studied GT transitions are limited by QEC 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.


Authors of this article thanks to the organizers of LASNPA-WONP-NURT 2017 October 23rd-27th 2017 Havana-Cuba for the organization and the support provided during the workshop.

Special thanks are owed to B. A. Brown, for his help in providing us the Oxbash code (Windows Version), and to M. H. Jensen, for the documents and the information provided about the interaction jj45apn.


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Received: February 13, 2018; Accepted: May 29, 2018

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