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Gamow-Teller Strength Distribution in Proton-Rich Nucleus $^{57} $ Zn And

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Gamow-Teller Strength Distribution in Proton-Rich Nucleus $^{57} $ Zn And Gamow-Teller strength distribution in proton-rich nucleus 57Zn and its implications in astrophysics Jameel-Un Nabi 1 • Muneeb-Ur Rahman Abstract Gamow-Teller (GT) transitions play a pre- on 57Zn are compared to the seminal work of Fuller, eminent role in the collapse of stellar core in the stages Fowler and Newman (FFN). The pn-QRPA calculated leading to a Type-II supernova. The microscopically β+-decay rates are generally in good agreement with calculated GT strength distributions from ground and the FFN calculation. However at high stellar tempera- excited states are used for the calculation of weak decay tures the calculated β+-decay rates are almost half of rates for the core-collapse supernova dynamics and for FFN rates. On the other hand, for rp-process condi- probing the concomitant nucleosynthesis problem. The tions, the calculated electron capture (β+-decay) rates B(GT) strength for 57Zn is calculated in the domain of are bigger than FFN rates by more than a factor 2 (1.5) proton-neutron Quasiparticle Random Phase Approxi- and may have interesting astrophysical consequences. mation (pn-QRPA) theory. No experimental insertions were made (as usually made in other pn-QRPA calcula- Keywords weak-interaction rates; electron capture tions of B(GT) strength function) to check the perfor- and beta decay, pn-QRPA theory; GT strength distri- mance of the model for proton-rich nuclei. The calcu- bution, rp-process. lated B(GT) strength distribution is in good agreement with measurements and shows differences with the ear- lier reported shell model calculation. The pn-QRPA 1 Introduction model reproduced the measured low-lying strength for 57 Zn better in comparison to the KB3G interaction The weak interactions and gravity are the guru that used in the large-scale shell model calculation. The stel- drive the evolution of heavy mass stars and the con- lar weak rates are sensitive to the location and structure comitant nucleosynthesis, which has been the subject of these low-lying states in daughter 57Cu. The struc- of much computation. The incarnation of the core- ture of 57Cu plays a sumptuous role in the nucleosyn- collapse mechanism is the conversion of a fraction of arXiv:1203.4669v1 [nucl-th] 21 Mar 2012 thesis of proton-rich nuclei. The primary mechanism the gravitational energy into kinetic energy of the ejecta for producing such nuclei is the rp-process and is be- and internal energy of the inner core of the exploding lieved to be important in the dynamics of the collapsing star (1). This inner core is mainly composed of iron supermassive stars. Small changes in the binding and excitation energies can lead to significant modifications group nuclei and when this inner core exceeds the ap- of the predictions for the synthesis of proton rich iso- propriate Chandrasekhar mass limits it becomes un- topes. The β+-decay and electron capture (EC) rates stable and inaugurates the implosion of the inner core and consequently announces the death of the star in a catastrophic explosion. The relic is either a neutron Jameel-Un Nabi star or black hole depending on the mass of the pro- Faculty of Engineering Sciences, GIK Institute of Engineer- genitors. If the stars are not too massive then they ing Sciences and Technology, Topi 23640, Swabi, Khyber Pakhtunkhwa, Pakistan collapse and consequently bounce and explode in spec- Muneeb-Ur Rahman tacular visual display commonly known as type-II or Department of Physics, Kohat University of Science and Tech- Ib/c supernovae. The collapse of the star is very sen- nology, Kohat 26000, Khyber Pakhtunkhwa, Pakistan sitive to the entropy and to the number of leptons per 1Corresponding author email : [email protected] baryon, Ye (2; 3). The neutrinos are considered as main sink of energy and lepton number until the core density 2 reaches around 1010g − cm−3. At later stage of the col- that it is likely possible that the neutrino-induced rp- lapse this assumption is no longer legitimate as weak process takes place in all core-collapse supernovae and interaction rates increase with increase of stellar core other astrophysical sites such as collapsar jets or disk density. For densities > 1011g − cm−3, the neutrinos winds formed around a black hole. In reference (7) the mean free paths become shorter and consequently they authors discovered an extremely luminous X-ray out- proceed through all phases of free streaming, diffusion, burst that marked the birth of a supernova of Type Ibc. and trapping. The most tightly bound of all the nuclei They attributed the X-ray outburst to the break-out of in the inner core of star is 56Fe (4) and further fusing the supernova shock-wave from the progenitor. of the nuclei is highly endothermic. The second bot- The open shell nuclei with a few nucleons outside a tleneck to the synthesis of heavier elements is the high doubly magic shell closure are of colossal interest to test Z number which poses high coulombic barrier for the the nuclear model predictions. 57Cu is of paramount charged particles to initiate nuclear reactions at stellar importance in this regard to test the pn-QRPA predic- core temperatures. This impediment to further nucle- tions. The pf -shell nucleus 57Cu has a single proton osynthesis is rescinded with the help of neuron capture just above the closed core of even-even 56Ni with Z = processes in the stellar core to form heavier isotopes N = 28. This simple structure permits far more accu- beyond iron group nuclei. These processes are further rate model calculations than are possible in the mid- classified into slow (s-) and rapid (p-) neutron capture dle of a nuclear shell. In particular, a comparison of processes depending on the neutron capture time scale the low-lying levels of 57Cu with the well-determined 57 τn and beta decay time scale τβ for nucleus to endure excited states of its mirror nucleus Ni is important beta decay. As discussed earlier that weak interaction for studying the charge symmetry of the nucleus. The and gravity are the mentor that drives the stellar evo- doubly magic nature of 56Ni confers it a stable struc- lutionary process and its subsequent death in a cat- ture and elements beyond 56Ni are cooked in the stellar aclysmic explosion. The main weak interaction pro- pot only via 56Ni(p, γ)57Cu reaction. The authors in cesses that play an effective role in the stellar evolution Ref. (8) pointed out that the structure of 57Cu plays are beta decays, electron and positron capture processes a sumptuous role in the nucleosynthesis of proton-rich and neutrinos emission/capture processes subject to the nuclei. This points the fact that this reaction rate is physical conditions available for these processes in the susceptible to the structure of 57Cu and environs nuclei, stellar core. These weak decay processes are smitten by including their binding energies. The primary mecha- Fermi and Gamow-Teller (GT) transitions. Fermi tran- nism for producing such nuclei is the rp-process and is sitions are straightforward and are important only for believed to be important in the dynamics of the col- beta decays. For nuclei with N >Z, Fermi transitions lapsing supermassive stars and x-ray bursts (9). The are Pauli blocked and the GT transitions dominate and rp-process is characterized by proton capture reaction their calculation is model dependent. Spin-isospin-flip rates that are orders of magnitude faster than any other excitations in nuclei at vanishing momentum transfer competing process, specially β-decay rates. The reac- are commonly known as GT transitions. These transi- tion path follows a series of fast (p,γ)-reactions until tions are ideal probe to test nuclear structure and play further proton capture is inhibited, either by negative preeminent role in the nucleosynthetic origin of the el- proton capture Q-values (proton decay) or small posi- ements in the late phases of the stellar life. When the tive proton capture Q-values (photodisintegration). As stellar matter is degenerate then the phase space for electrons captures in the stellar pot assist the cooking the electron in beta decay is Pauli blocked and electron process and gravity, therefore, it is crucial to know the captures become dominant in the stellar core producing nuclear structure properties of the doubly magic shell neutrinos which escape from the surface of the star and 56Ni and nuclei in its vicinity. These nuclei drive the takes away the core energy and entropy as well. These electron capture processes in the dense core of heavy electron capture rates and β+ decay rates are very sen- mass stars. The beta decay rate calculations require sitive to the distribution of the GT+ strength which is the evaluation of the GT strengths for many levels per responsible for changing a proton into a neutron (the nucleus. The pn-QRPA theory gives us the emanci- plus sign is for the isospin raising operator (t+), present pation to use model space as big as 7 ~ω rather than in the GT matrix elements, which converts a proton truncated model spaces usually employed in some shell into a neutron). The authors in (5; 6) took the accurate model calculations. neutrino transport into account in their hydrodynamic Earlier the half-lives for β+/EC decays for neutron- studies of core-collapse supernovae and showed that the deficient nuclei with atomic numbers Z = 10 - 108 were bulk of the neutrino-heated ejecta is proton-rich during calculated up to the proton drip line for more than 2000 the early phase (≤ 1s). Their studies also provided nuclei using the same model (10). These microscopic 3 calculations gave a remarkably good agreement with the total electron capture rate and a microscopic cal- the then existing experimental data (within a factor culation of excited state GT strength distributions is of two for more than 73% of nuclei with experimental desirable.
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