Nuclear structure of In isotopes in Sn mass region

The monopole effect resulting from the interaction between the magic core and the valence particles has a particular interest in the study of nuclear structure. To understand the importance of this interaction, we have realized some spectroscopic calculations for odd-odd In isotopes containing one hole proton and few neutron particles in addition to Sn doubly magic core in their valence spaces. The using interaction is derived from jj45apn one taking into account the monopole interaction in the studied mass region, and using recent single particle and hole energies. The calculations are performed in the framework of the nuclear shell model by means of Oxbash nuclear structure code.


Introduction
The region around the last magic N=Z nucleus 100 Sn, close to the path of rp-process, was the main of several theoretical and experimental works that aimed to give a global description of nuclear structure. With their one proton hole and few particle neutrons, Odd-Odd indium isotopes, near 100 Sn doubly magic core, are of great importance in nuclear structure studies. They give opportunity to develop our knowledge about protonneutron interaction near astrophysical processes pathways. 102 In was identified for the first time by Béraud et al. [1,2]. They studied the A=102 isobars using an on-line mass isotopic separator operating on nuclear reactions induced by heavy ions. This isotope was produced by means of the reaction 92 Mo ( 14 N, 4n), and the half-life of 24(4) s is measured. Martín et al. [3] have investigated nuclei in end-point region of the rp-process near 100 Sn using direct mass measurements at SHIPTRAP by the Penning trap mass spectrometer at GSI Darmstadt, where they experimentally identified three nuclides for the first time. The mass excess of 102 In is determined to be -70694(12) keV, which is different by 16 keV from the given value Audi et al. [4]. In 2009, Elomaa et al. [5] have realised a mass filter of nuclei produced via proton and 3 H induced fusion-evaporation reactions in 100 Sn region. They have measured a new mass excess -70690.4(54) keV which is different by 4 keV from the previous one. This nucleus was the subject of a theoretical study in Ref. [6]. In which, Karny et al. have performed spectroscopic calculations of the b-decay of 102 Sn within the p(2p 1/2 ,1g 9/2 ) n(1g 7/2 , 2d 5/2 , 2d 3/2 , 3s 1/2 , 1h 11/2 ) model space, and using SNC interaction [7]. In comparison with the experimental data, this interaction has reproduced the spin and parity of the ground state 6 + and the three first excited states. However, the calculated energies for In 1977, Varley et al. presented the discovery of 104 In [2,8]. They have realised measurement of half-lives, excitation functions, g-x-ray and g-g coincidences in order to determine the energetic spectrum of 104 In. The measured half-life of the isomer was estimated to be 1.5(0.2) min. Szerypo et al. [9] studied the beta decay of 104 Sn at GSI, by means of 58 Ni+ 50 Cr reaction in order to evaluate the energetic spectrum of the 104 In descendent. Few years later, Karny et al. [6] have studied the beta decays of 102-104 Sn and their 102-104 In descendents using high-resolution germanium detectors as well as a Total Absorption Spectrometer (TAS). Elomaa et al. [5] have measured the mass excess of 104 In -76176.5(51) keV with a difference of 66 keV from the given one in [4]. The experimental spectra of these two isotopes are presented

Theoretical framework
The interactions the supposed inert core with the adding nucleons can lead to shell evolution and modification of the spectroscopic properties of nuclei near around this core [10][11][12]. Poves and Zuker [13] have introduced the description of the monopole effect, in which the Hamiltonian of the system is 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 have proposed to express the monopole Hamiltonian of the system in terms°: [14][15][16], s and/or t denote a proton and/or a neutron orbit. n s, t and T s, t refer, respectively, to the number and the isospin operator defined by Zuker [10,15] as a function of the monopole Hamiltonian diagonal part ' st V tt [12]. This amount can be defined as a function of the average two body matrix elements (TBMEs), of a given effective interaction V J (j s j t ), over the configurations of s and t orbits [12,14], Here, t (t') 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 [17,18]). These TBMEs are used in order to calculate the monopole term (Eq. TBMEs. These TBMEs are 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 properties of 102-104 In isotopes.

Results and discussion
In this work, we have performed shell model calculations, by means of the new interaction jj45m in p and n(0g 7/2 , 1d 5/2 , 1d 3/2 , 2s 1/2 and 1h 11/2 ) N-50 model space in 100 Sn 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 [19,20].
The calculations for 102 In nucleus using jj45m interaction, shown in Fig. 2, allow to reproduce the parity of the low laying states. However, this interaction gives 7 + as a ground state, which is different from 6+, the experimental one. The original interaction gives negative parity for the low laying states.
Neither the energetic excited states, nor the experimental sequence are reproduced using the two interactions for 104 In nucleus. However, the original interaction lead to reproduce the levels sequence except the 6 + state, which is situated between 4 + and 8 + states.
The reduced electromagnetic transition probabilities can be expressed in terms of the electromagnetic TBMEs M ( B sl sl Table 1 and 2 show the electromagnetic properties evaluated by means of jj45apn and jj45m interactions, for the studied nuclei. The calculated values of reduced electric transition probabilities B(E2) are obtained using e p =1.50e and e n = 0.50e for the effective charges. For the magnetic moments µ J , we have used the free g factors. These results show that the two interactions give different values for the electromagnetic properties. However, the obtaining mean lives are close for 104 In.