#### Transcript b-Decay Rates of Nuclei in Ground and Excited States and

b-Decay Rates of Nuclei in Ground and Excited States and Effects on the r-Process of Nucleosynthesis b-Decay rates of excited-state nuclei are calculated using a single-particle model, which incorporates shell energies of individual nucleons into the mass formula. Energies of two-particle levels are calculated by assuming a Fermi gas model with shell and pairing forces. A comparison of level energies to those of the spherical shell model for nuclei of the same mass yields a determination of a configuration mixture of spherical shell model eigenstates characterized by their quantum numbers. Therefore, the order of the decay is specified. The resulting density of particle states is inserted into the gross theory of b-decay, so the ease of calculation is maintained with the decay form factors. This model is quite useful in that bdecays of excited state nuclei, which are created by the promotion of nucleons to levels above the Fermi surface, can be calculated with the same method. The ultimate purpose of this calculation is to determine the effects of b-decays on the rprocess of nucleosynthesis. Since r-process progenitor nuclei are very neutron rich, decay rates must be calculated, and current models have utilized only ground-state nuclear decay rates. The possibility of a faster progression along the r-process path, as well as the possible elimination of closed-shells in a small population of the N=82 nuclei due to excitations above the shell may create an r-process simulation in which the mass 195 nuclei are produced in greater abundance by the time the rprocess freezes out. An r-process model which evolves average b-decay rates as a function of temperature is used. The environmental parameters of this model simulate those of the supernova hot-bubble region, a strong candidate for the rprocess site. The final freezeout abundance distribution is compared with that of the solar system r-process abundance distribution. R.N. 1,2 Boyd , r-Process Results Nearly four decades have passed since the r-process was postulated. The nature of the distribution of heavy elements in the solar system (left) lead to the theory that these elements were produced via neutron captures on seed nuclei, producing the r-process path through very neutron-rich nuclei (right). A comparison of the distribution of r-process elements in the solar system to that of the metal-poor halo stars (below-right) indicates that the r-process is both primary and unique. An r-process site that has met nominal success is the supernova hot-bubble region (left) above a nascent neutron star. Difficulties in current rprocess calculations include their ability to successfully produce the A~195 peak in the solar distribution (above-left). [Cowan et al. (1990)] dN1 M (E) D ( E , ) W ( E , )d o ( E ) d mc 3 7 2 0 1 dN1 Q o D ( E ) d W ( E , ) f ( E )ddE Average Decay Rates vs. Temperature dN ni i d i W i , k nk i k NP me w i; n, l , j 2 1 n ,l , j • Each level is a sum of shell model Eigenstates with coefficient w(i;n,l,j). • Two-particle levels. Excited states achieved by calculating levels above the Fermi surface. • Transition probability function - Can the specified transition take place, and with what strength? • Transition Matrix Elements – Takes state availability into account. • Nuclei at T0 – Not necessarily in the ground state. – Distribution of nuclei in excited states: • Stellar environments • r-Process effects – Increased b-decay rates – Change in many reaction Q-values? i w i; n, l , j n ,l , j n ,l , j D E, D f , i w i; w f ; , , 100 10 1 Pd-128 M E M i k 2 i ,k , , Sn-135 La-164 Te-150 Pr-171 Tm-195 0.1 2 0 ni nkw i; w k ; , g 1 2 3 4 5 6 7 8 9 10 Temperature (Billion Kelvin) Accuracy of Calculated Decay Rates (Ground State) 3 Energetically Possible Decays Single-Particle States in the Gross Theory Neutrons Protons (Ln 0.5, Ye =0.4) 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 s-Process Peak r-Process Peak [Schramm (1982)] 1.E-08 Excited State Decays 1.E-09 80 140 160 180 200 220 Conclusions [Sneden et al. (1996)] Effects of excited state b-decays on the r-process – Relaxes some constraints – No artificial adjustments to parameters (e.g., entropy) needed – “Fine Tuning” of the r-process distribution via b-delayed neutron emission and freezeout interactions Future Work – Improvement of decay rate calculations – Experiment in progress • Type II Supernova Model in the Schwarzchild Geometry • Full Network Calculation (Kajino et al. 1999) –~3700 Nuclei from A=1-240 from b-Stability to the Neutron Drip Line –Extensive network continuous between a-process and rprocess • Simulation Until Well Beyond Freezeout • b-Decays Given as Functions of Temperature References Kondoh, T., Tachibana, T., Yamada, M., Prog. Theor. Phys. 72, 708 (1985). Nakata, H., Tachibana, T., Yamada, M., Nuc. Phys. A 625, 521 (1997). Otsuki, K., Tagoshi, H., Kajino, T., Wanajo, S., ApJ 533, 424 (2000). Schramm, D.N., in Essays in Nuclear Astrophysics, ed. Barnes, C.A., Clayton, D.D., Schramm, D.N., (Cambridge Univ. Press), p. 325 (1982). Sneeden, C., McWilliam, A., Preston, G.W., Cowan, J.J., Burris, D.L., Armosky, B.J., ApJ 467, 819 (1996). Tachibana, T., Yamada, M., Yoshida, Y., Prog. Theor. Phys. 84, 641 (1990). 2 Q 1 1Department 0 -1 -2 [Otsuki et al. (2000)] Z 120 Solar A Even-Even Odd-Z Odd-N Odd-Odd N 100 Ground State Decays The Network Calculation 1000 Average Decay Rate (1/s) 5 4 LOG(Calc. Rate/Exp. Rate) • Continuous distribution of nuclear states • Fermi and Gamow-Teller transitions (and thus, the transition matrix elements) are continuous functions of transition energy • Decay rates are products of: – Transition probability – Nucleons available for decay in parent state – Availability of states for available nucleons to decay to – Fermi function 1 2 r-Process Results The r-Process b-Decays, Excited States, and the r-Process The Gross Theory of b-Decay and T. 3-5 Kajino Abundance M.A. 1 Famiano , -3 0.0001 0.001 0.01 0.1 Experimental Rate (1/s) 1 10 100 of Physics, Ohio State University, Smith Lab, 174 West 18th Avenue, Columbus, OH 43210; [email protected]; [email protected] 2Department of Astronomy, Ohio State University, McPherson Laboratory, 140 West 18th Avenue, Columbus, OH 43210-1173 3National Astronomical Observatory, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan; [email protected] 4Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyoku, Tokyo 113-0033, Japan 5Department of Astonomical Science, Graduate University for Advanced Studies, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan