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THE BIG DIPexperimental and systematic
discussions of neutron binding in very neutron-rich nuclides
William B. Walters
Department of Chemistry
University of Maryland
• 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.
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/Maryland and ALEX BROWN from Michigan State.
Reviews of Modern Physics, 29, 47 (1957).
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.
Cd48 76
124
4+
6+
613
0
1385
2140
Cd48 78
126
0+
2+
4+
0
Cd48 80
128
0+ 0
652
2+ 14281467
652
814
5± 1847 5± 1869
2+ 645645
4+ 1429784
401
0+
2+
Cd48 82
130
0+ 0
Evidence for shell quenching
0
500
1000
1500
2000
0
0.5
1
1.5
2
2.5
3
45 50 55 60 65 70 75 80 85
CdPd
Te
Cd
Te
Pd
4+/2+ ratio
+2 energies (keV)
calculated
calculated
Pd calculations:Kim, Gelberg,Mizusaki, Otsuka, von Brentano,NP A 604,163 (1996).
T. Kautzsch, et al., E. P. J. A 9, 201 (2000).
963
0
798
0
645
0
491
d5/2
370
332
0
160
0
270
0
527
0
724
0
815
0
851
00000
832769
g7/2
0 0
1806
0
g7/2d5/2d5/2 g7/2d5/2A = 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 207
N = 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 126
Monopole shift in odd-mass Sb nuclides.
282
J. Shergur et al., PRC 65, 034313 (2002)
Decay of Sn-135 to levels of Sb-135 RILIS (CERN/ISOLDE)
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 (,n) and (n, ) 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.
Now, I want to describe some details about the (,n) = (n, ) equilibrium that show where and how nuclear structure and decay properties on nuclei play a role in r-process movement.
(,n)(n, )
decay
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 108N = 62 63 64 65 66 67 68 69 70 71 72
Sn = 2.5 for 104Rb67…the process moves on.
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.
Kr half-lives 104(46) 48 23 15 9 5 ms.
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.
You can also see that below Z = 44, the half-lives are so short that there is very little waiting.
With these half-lives, “waiting starts atZ = 44, Ru, and increases toward the major blockade in this mass region,130Cd.
Finally, at 132In, the Sn is sufficiently high to permit neutron capture to proceed on to the next waiting point, 135In
Half life (ms)
Half life (ms)Neutron separationEnergy (MeV) Sn
Conclusion: The critical values from nuclear structure and decay measurements that are needed are half-lives and neutron separation energies (masses).
P. Möller, J. R. Nix, and K.-L. Kratz, ADNDT 66, 131(1997).
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Sn (MeV)
Znuclides N = 82 N = 83
49 In=131 132 227 2016.2 2.7
48 Cd 130 131 165 686.2 2.0
47 Ag 129 130 46 425.6 2.0
46 Pd 128 129 56 1175.5 1.5
45 Rh 127 128 22 185 1.2
44 Ru 126 127 34 364.9 0.7
43 Tc 125 126 9 84.3 0.7
42 Mo 124 125 11 94.2 0.1
41 Nb 123 124 3.5 4.13.4 0.08
40 Zr 122 123 4.3 3.83.6 -0.6
-2
0
2
4
6
8
10
12
50 55 60 65 70 75 80 85
Neutron Separation Energies
ZrKrRuSn
Sep
arat
ion
Ene
rgy
in M
eV
Neutron Number
From Möller, Nix and Kratz, ANDT 66, 131 (1997).
In particular, it is the flattening of the separation energies for theZr (and adjacent) nuclides that results in the large dip in yields for the A = 120 region.
Observe that there is NO leveling for theSn nuclides!!!!
The Sn points areExperimental.
d 5/2 7/2g
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
f
p
p
s1/2
5/2
h11/2
1/2
3/2
3/2d
g
N
Z
Heaviest known yrast structures Heaviest known half lives
160 ms 46 ms56 ms22 ms
9/2
34 ms 9 ms11ms 3 ms 4 ms
11/2- 21703/2+ 2042
1/2+ 1205
131 Sn50 81
7/2+ 2201
7/2+ 2434
91 Zr40 51
5/2+ 0 5/2+ 1654
1/2+ 331
11/2- 50(75)3/2+ 0
Neutron monopole shifts from Zr-90 to Sn-132
3/2+ 11037/2+ 1264
5/2+ 1400
11/2- 2268
97 Zr40 57
1/2+ 0
121 Zr40 81
5/2+ 3000
11/2- 0
3/2+ 1200
7/2+ 2000
1/2+ 1800
extrapolatedAdding six moreN = 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 theN = 3 shell protons.
11/2- -1003/2+ 0
1/2+ -1340
7/2+ +110
91Zr40 51
5/2+ -2760
Neutron monopole shifts from Zr-90 to Gd-145
Neutron levels normalized to the d-3/2 particle.
N = 81 hole nomalized to thed-3/2 hole in Sn-131.11/2- +900
3/2+ 0
1/2+ -1600
7/2+ -70
97Zr40 57
5/2+ -3080
11/2- -50(75)
3/2+ 0
1/2+ -331
7/2+ -2434131Sn50 81
5/2+ -1654
extrapolated
11/2- +1000
3/2+ 0
1/2+ -6507/2+ -500
121Zr40 81
5/2+ -2000
11/2- -334
3/2+ 0
1/2+ -308
133 Te52 81
11/2- -526
3/2+ 0
1/2+ -288
135Xe
54 81
11/2- -661
3/2+ 0
1/2+ -283
Ba56 81
137
11/2- -754
3/2+ 0
1/2+ -255
Ce58 81
139
11/2- -757
3/2+ 0
1/2+ -194
Nd60 81
141
11/2- -754
3/2+ 0
1/2+ -110
Sm62 81
143
11/2- -722
3/2+ 0
1/2+ +27
Gd64 81
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
pf proton core
pf neutron core
10 g9/2 neutrons
6 d5/2 neutrons
8 g7/2 neutrons
12 h11/2 neutrons
little neutron skin
BIG neutron skin
Adding 10 g9/2 protons
Adding 8 g7/2 protons
In other words, it takes ALL 18 g9/2 protons to fully bind the 12 h11/2 neutrons.
Binding of various layers of neutrons by pf shell protons.
40 Zr 4080
40 Zr 5090
40 Zr 5696
40 Zr 70110
40 Zr 82122
50 Sn 82132
58 Ce 82140
11/2- -50(75)
3/2+ 0
1/2+ -331
7/2+ -2434
131Sn50 81
5/2+ -1654
N = 81 hole nomalized to thed-3/2 hole in Sn-131.
11/2- -334
3/2+ 0
1/2+ -308
133 Te52 81
11/2- -526
3/2+ 0
1/2+ -288
135Xe
54 81
11/2- -661
3/2+ 0
1/2+ -283
Ba56 81
137
11/2- -754
3/2+ 0
1/2+ -255
Ce58 81
139
11/2- -757
3/2+ 0
1/2+ -194
Nd60 81
141
11/2- -754
3/2+ 0
1/2+ -110
Sm62 81
143
11/2- -722
3/2+ 0
1/2+ +27
Gd64 81
145
11/2- -679
3/2+ 0
1/2+ +72
Dy66 81
147
11/2- -631
3/2+ 0
1/2+ +111
Er68 81
149
(749)(751)
(742)
In this region as Z increases from 50 to 58, the protons are filling the g7/2 orbitals, and then from 58 to 64 the protons are filling the d5/2 orbitals.
Starting at Z = 65, the protons are fillingthe s1/2, d3/2, h11/2 orbitals.
The h-11/2 neutrons seem insensitive to h-11/2 protons!!
133Sn
7/2- 0
3/2-854
9/2-
1561
1/2-1656
5/2-
2004
134Te
0+
2+1280
135
3/2-
658
137
3/2-
601
9/2-1220
1/2-
5/2-
986
Te136
Xe
2+1313
Xe139
3/2-
627
9/2-1283
1/2-
5/2-
1082
138
2+
Ba Ba
13/2+16199/2-
141
3/2-
662
9/2-13551/2-
5/2-
1137
140
2+
Ce
1596
13/2+
19159/2-
Ce143
3/2-
742
9/2-14071/2-
5/2-
1306
142
2+
Nd
1575
13/2+
17399/2-
Nd145
3/2-
893
9/2-
1423
1/2-5/2-
144
2+
Sm
1660
13/2+
9/2-
Sm147
3/2-1152
9/2-
1397
1/2-
146
2+
Gd
1971
13/2+
9/2-
Gd 149
3/2-
9/2-
1/2-
148
2+
Dy
1677
13/2+
9/2-
Dy 151
3/2-
9/2-
801
1/2-
150
2+
Er
1578
13/2+
9/2-
153
9/2- 567
152
2+
Yb
1531
13/2+
9/2-
Er Yb154
2+
Hf
1513
N =83 ISOTONES
7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+
1220
9/2-1246
1/2- 1083
1436
1035 984
5/2-1091
13/2+
2625
1423
13/2+
2713
1774
C2S =6
C2S =3
C2S =6
C2S =4
1846
g7/2 protons d5/2 protons h11/2 protons
νh9/2
Sn50 83
1337/2- 0
3/2- 854
νh9/2 15619/2-
νp3/2
νf7/2
1/2- 1656νp1/2
5/2- 2004νf5/2
13/2 + 2694(200)νi13/2
Sn = 2455 (45)
0νf7/2
normall2νf7/2
νf7/2
0.7 l2 0.4 l2
854νp3/2
νp3/2
νp3/2
1561νh9/2
νh9/2
νh9/2
1656νp1/2
νp1/2
νp1/2
2004νf5/2 νf5/2νf5/2
2694νi13/2
νi13/2 νi13/2
0
154
2561
946
1920
3800
0
-500
3600
250
1850
5000
Sn50 96146
Sn50 102
152
Pb82 125207
7/2- 0
3/2- 1442
νh9/2 -10739/2-
νp3/2
νf7/2
1/2- 2340νp1/2
5/2- 1770νf5/2
13/2 + 708νi13/2
3/2- 0
1/2- 2023
5/2- 3991
49
20 29Ca
9/2+ 6000
3/2- 0
1/2- 11125/2- 769
57
28 29Ni
9/2+ 3009
3/2- 1095
1/2- 588
5/2- 1451
89
40 49Zr
9/2+ 0
1/2- 0
3/2- -1140
5/2- -694
67
28 39Ni
9/2+ 10079/2+ - 5/2- gap ≥ 2 000 keV
9/2+ - 5/2- gap =1700 keV
9/2+ - 5/2- gap = ~2200 keV9/2+ - 5/2- gap = ~1500 keV
7/2- -75007/2- -65007/2- -55007/2- -2500
3/2- -100043
14 29Si
7/2- 0
1/2- 1000
5/2- 6000
New Shell Gapat N = 34???
Monopole shift of the p3/2 and p1/2 neutron orbitals with changing nuclear size and N/Z ratio.
ProjectedProjected
Possible double magic nuclide 48Si34
W. B. Walters, Seyssins, France, AIP Conference Series 447, 196 (1998).
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.
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.
Sn
In
Cd
Ag
Pd
Rh
Ru
Tc
Mo
Nb
Zr
Y
Sr
Rb
Kr
Br
Se
As
Ge
Ga
Zn
Cu
Ni
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82
ε ≈ 0.4
f
p
p
s1/2
5/2
9/2
h11/2
1/2
3/2
3/2dd5/2
A = 112 A = 124
N = 2 Z
g
N →
↑Ζ
r processpath
N = 1.6 Z
Heaviest known yrast structures