William B. Walters Department of Chemistry University of Maryland

1. THE BIG DIPexperimental and systematic discussions of neutron binding in very neutron-rich nuclides William B. Walters Department of Chemistry University of Maryland

2. First, let me thank the JINA group for the kind invitation to talk about neutron-rich nuclides here in Michigan at Gull Lake. • It is a real privilege to speak to an audience that includes people who can and and probably will be able to test some of these ideas in future experiments.

3. I am just back at Maryland after a 6-month Sabbatical visit in Mainz that was made possible by a Research Award from the Alexander von Humboldt Stiftung . First, I wish to thank Professor Karl-Ludwig Kratz, for his efforts with AvH and Mainz that made the visit in Mainz possible, and both he and Gisela for making the visit interesting and enjoyable And, also the U. S. Department of Energy who has provided strong support for the Maryland part of this work. I also must acknowledge the hard work, long discussions, and continuous efforts of BERND PFEIFFER, PETER MÖLLER, DAREK SEWERYNIAK, and ANDREAS WÖHR and a large group of Mainz, Maryland, ISOLDE and Argonne students and post docs, along with many detailed theoretical discussions with both JIRINA RIKOVSKA from Oxford/Marylandand ALEX BROWN from Michigan State.

4. Since BBFH showed in the Figure at the left the connection between elemental abundances the location of closed neutron shells, study and knowledge of the structure and decay of those nuclides involved in nucleosynthesis has been entwined with astrophysical considerations about how, when, and where nucleosynthesis takes place. Reviews of Modern Physics, 29, 47 (1957).

6. T. Kautzsch, et al., E. P. J. A 9, 201 (2000). Evidence for shell quenching Pd calculations: Kim, Gelberg, Mizusaki, Otsuka, von Brentano, NP A 604,163 (1996).

7. J. Shergur et al., PRC 65, 034313 (2002) Decay of Sn-135 to levels of Sb-135 RILIS (CERN/ISOLDE)

8. K.-L. Kratz, B. Pfeiffer et.al

9. Today, I come from the Kratz,Thielemann, Möller, etc.,school of nuclear astrophysics. The basic assumptions about the r-process that underlie the discussion are that r-process must take place in a neutron-rich environment where: neutron densities must range up to 1027 to produce elements beyond lead, that at some point neutron densities are encountered at the level of 1020-23 to make the peak at A = 130 (at 1027, little would be left at A = 130), the temperature is over 109 K with an appropriate gamma ray flux, during the process equilibrium exists between (g,n) and (n, g) reactions, that the process ends very quickly…termed “freeze-out” and the nuclides left at the end undergo beta decay (with beta-delayed neutron emission) toward the line of stability. In particular, this process produces the “r-only” nuclides like 110Pd, 124Sn, and 130Te. that the yields shown in the abundance curve arise from material that is “waiting” to move on at “freeze-out” and subsequently decays back to stable nuclides with higher Z, that the peaks in the abundance curves arise from material that has accumulated at a “waiting-point” whose forward movement is “slowed down”, that valleys in the abundance curves arise from material where forward movement is quite rapid and, hence, there is little accumulated material to decay toward stability.

10. Sn = 5.0 2.3 4.5 2.1 4.3 1.9 4.1 1.3 3.4 0.9 2.5 36Kr 98 99 100 101 102 103 104 105 106 107 108 N = 62 63 64 65 66 67 68 69 70 71 72 Now, I want to describe some details about the (g,n) = (n, g) equilibrium that show where and how nuclear structure and decay properties on nuclei play a role in r-process movement. b decay (n, g) (g,n) Sn = 2.5 for 104Rb67…the process moves on. Kr half-lives 104(46) 48 23 15 9 5 ms. Waiting points always have even neutron numbers. If the neutron density is larger, the waiting point could move to 106. If the temperature is higher, the waiting point could move to 102.

11. P. Möller, J. R. Nix, and K.-L. Kratz, ADNDT 66, 131(1997). The decay and waiting responsible for the formation of the A = 130 peak is illustrated. What are shown are the half-lives and Sn values for the N = 82 And N = 83 isotones. As you can see, the neutron is unbound in 123Zr, whereas the neutron is rather tightly bound for all of the N = 82 isotones. Half life (ms) Sn (MeV) Sn (MeV) Sn (MeV) Sn (MeV) You can also see that below Z = 44, the half-lives are so short that there is very little waiting. Sn (MeV) Sn (MeV) Sn (MeV) With these half-lives, “waiting starts at Z = 44, Ru, and increases toward the major blockade in this mass region, 130Cd. Sn (MeV) Sn (MeV) Half life (ms) Neutron separation Energy (MeV) Sn Finally, at 132In, the Sn is sufficiently high to permit neutron capture to proceed on to the next waiting point, 135In Conclusion: The critical values from nuclear structure and decay measurements that are needed are half-lives and neutron separation energies (masses).

12. Neutron Separation Energies Observe that there is NO leveling for the Sn nuclides!!!! 12 The Sn points are Experimental. 10 Zr Kr Ru Sn 8 6 In particular, it is the flattening of the separation energies for the Zr (and adjacent) nuclides that results in the large dip in yields for the A = 120 region. Separation Energy in MeV 4 2 0 -2 50 55 60 65 70 75 80 85 Neutron Number From Möller, Nix and Kratz, ANDT 66 , 131 (1997).

14. Adding six more N = 4 shell d-5/2 neutrons beyond the ten g-9/2 neutrons leads to a neutron skin that inhibits the binding of the N = 5 oscillator shell h-11/2 neutrons by the N = 3 shell protons.

15. Continued addition of g7/2 protons Beyond Z = 50 continues to result in stronger binding for the h11/2 neutron up through Z = 58 145

16. Binding of various layers of neutrons by pf shell protons. 96 90 80 40 Zr 40 40 Zr 56 40 Zr 50 132 122 110 140 50 Sn 82 40 Zr 82 40 Zr 70 58 Ce 82 pf proton core Adding 10 g9/2 protons pf neutron core 10 g9/2 neutrons 6 d5/2 neutrons little neutron skin 8 g7/2 neutrons BIG neutron skin 12 h11/2 neutrons Adding 8 g7/2 protons In other words, it takes ALL 18 g9/2 protons to fully bind the 12 h11/2 neutrons.

17. The h-11/2 neutrons seem insensitive to h-11/2 protons!!

19. Acta Physica Pol. B 27, 475 (1996).

22. Conclusion: The “big dip” can be traced to what I believe is a calculated overbinding for the h-11/2 neutron orbitals between N = 70 and N =82. Data exist that can be interpreted to indicate that the binding of h-11/2 neutrons is quite sensitive to the number of g-7/2 ( and by inference, g-9/2 protons) in the nucleus, as well as the number of gdds neutrons present. The challenge for experimental science is to determine as many properties of these very neutron-rich nuclides as possible, and the challenge for theorists is to improve the way that nuclear models describe very neutron-rich nuclides. Stated another way…..RIA must be built with design goals that include the study of Zr-122 and neighboring nuclides. Thank you for your attention.

23. Deformation changes all of that for Sr and Zr by bringing g9/2 protons up from below Z = 40

24. We start with spherical 98Sr60 where shape coexistence is well known and arises from the 10 neutrons and four protons into downsloping orbitals. And you can see that the nucleus can take another pair of protons for Zr. The important point is that these shifts move 4 to 6 protons from the pf orbitals into the g9/2 orbitals and permit much better binding of the h11/2 neutrons. Adding 10 more neutrons up to N = 70 is seen to be rather neutral and perimts the g9/2 protons to stay up to that point. However, beyond N = 70, additional neutrons drive the nucleus back toward sphericity and drive the protons back into the pf shell, thereby once again loosening the binding for the h11/2 neutrons.

25. Notice that there IS a valley at A = 180…the N = 126 shell works.