THE BIG DIP
experimental 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 KarlLudwig 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.
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+
2140
5±
1847
2+
4+
2+
0+
1428
1385
613
0
5± 1869
401
4+ 1467 4+
814
784
652
2+
2+
652
0+
126
124
Cd
48
76 48
645
645
0
Cd
1429
0+
0
0+
0
128
130
Cd
Cd
78 48
80 48
82
T. Kautzsch, et al., E. P. J. A 9, 201 (2000).
2000
3
calculated
4+ /2+ ratio
2.5
Pd
Cd
1500
2
Evidence for
shell quenching
1000
Te
Te
1.5
Pd
1
Cd
500
calculated
0.5
2+ energies (keV)
0
45
Pd calculations:
Kim, Gelberg,
Mizusaki, Otsuka,
von Brentano,
NP A 604,163 (1996).
50
55
60
65
70
75
80
0
85
Monopole shift in odd-mass Sb nuclides.
J. Shergur et al., PRC 65, 034313 (2002)
1806
d5/2
Decay of Sn-135 to levels of Sb-135 RILIS (CERN/ISOLDE)
963
832
769
g7/2
851
815
798
724
645
527
491
332
270
282
160
0
0
0
0
0
0
0
0
0
37
0
0
0
0
0
0
54
56
58
60
62
64
66
68
70
72
74
0
g7/2
A = 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131
52
0
d5/2 g7/2
d5/2
N = 50
0
76
78
80
133
135
207
82
84
126
K.-L. Kratz, B. Pfeiffer et.al
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.
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)
Kr half-lives 104(46)
Sn = 2.5 for 104Rb67…the process moves on.
48
23
15
9
5 ms.
Sn = 5.0 2.3 4.5 2.1 4.3 1.9 4.1 1.3 3.4 0.9 2.5
99 100 101 102 103 104 105 106 107 108
36Kr 98
N = 62 63
64 65
66 67 68 69 70 71 72
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.
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.
nucZ
lides
With these half-lives, “waiting starts at
Z = 44, Ru, and increases toward the
major blockade in this mass region,
130Cd.
N = 83
4 9 I n=1 3 1 1 3 2
227
6 .2
48 C d 130 131
165
6 .2
68
2 .0
Sn (MeV)
46
5 .6
42
2 .0
Sn (MeV)
56
5 .5
117
1 .5
Sn (MeV)
22
5
18
1 .2
Sn (MeV)
34
4 .9
36
0 .7
Sn (MeV)
9
4 .3
8
0 .7
Sn (MeV)
11
4 .2
9
0 .1
Sn (MeV)
41 Nb 123 124
3 .5
3 .4
4 .1
0 .0 8
Sn (MeV)
4 0 Zr 1 2 2 1 2 3
4 .3
3 .6
3 .8 Half life (ms)
- 0 .6 Neutron separation
47 A g 129 130
46 Pd 128 129
4 5 Rh 1 2 7 1 2 8
You can also see that below Z = 44, the
half-lives are so short that there is very
little waiting.
N = 82
4 4 Ru 1 2 6 1 2 7
43 Tc 125 126
42 Mo 124 125
201 Half life (ms)
2 .7 Sn (MeV)
Energy (MeV) Sn
Finally, at 132In, the Sn is sufficiently high
Conclusion: The critical values
to permit neutron capture to proceed on to
from nuclear structure and decay
the next waiting point, 135In
measurements that are needed are
half-lives and neutron separation
energies (masses).
12
Neutron Separation Energies
The Sn points are
Experimental.
Separation Energy in MeV
10
8
Observe that
there is NO
leveling for the
Sn nuclides!!!!
Zr
Kr
Ru
Sn
6
4
2
0
-2
50
55
60
65
70
75
Neutron Number
From Möller, Nix and Kratz, ANDT 66, 131 (1997).
80
85
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.
Heaviest known yrast structures
Heaviest known half lives
Sn
In
Cd
g 9/2
160 ms
46 ms
56 ms
22 ms
34 ms
9 ms
11ms
3 ms
4 ms
1/2
Ag
Pd
Rh
Ru
Tc
Mo
Nb
p
Zr
Y
Sr
p 3/2
Rb
Kr
Br
Se
f 5/2
As
Ge
Ga
Zn
Cu
Ni Z
N
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
d 5/2
s1/2
g
7/2
d 3/2
h 11/2
7/2+ 2434
extrapolated
5/2+
0
91
Zr 51
40
5/2+ 1400 5/2+ 3000
1/2+ 1205
1/2+
0
97 Zr
57
40
3/2+ 2042
11/2- 2170
7/2+ 2201
7/2+ 2000
1/2+ 1800
3/2+ 1200
3/2+ 1103
7/2+ 1264
11/2- 2268
Adding six more
5/2+ 1654 N = 4 shell d-5/2
neutrons beyond the
ten g-9/2 neutrons
leads to
a neutron skin
1/2+ 331
that inhibits the
11/2- 50(75)
binding of the N = 5
3/2+ 0
131 Sn
oscillator shell
81
50
h-11/2 neutrons by the
N = 3 shell protons.
11/20
121
Zr 81
40
Neutron monopole shifts from Zr-90 to Sn-132
Neutron monopole shifts from Zr-90 to Gd-145
Neutron levels normalized to the d-3/2 particle.
Continued addition of g7/2 protons
Beyond Z = 50 continues to result
in stronger binding for the h11/2
neutron up through Z = 58
extrapolated
11/2- +900
7/2+ +110 3/2+ 0
3/2+ 0 7/2+ -70
11/2- -100
3/2+
0
7/2+ -500
1/2+ -650
1/2+ -1340
1/2+ -1600
5/2+ -2760
5/2+ -3080
91
40Zr51 97
40Zr57
N = 81 hole nomalized to the
d-3/2 hole in Sn-131.
11/2- +1000
5/2+ -2000
3/2+ 0 3/2+ 0
11/2- -50(75) 1/2+ -308
1/2+ -331
11/2- -334
3/2+
0
3/2+
0 3/2+
0 3/2+
0
3/2+
0
1/2+ +27
3/2+
1/2+ -288
11/2- -526
+
1/2+ -283 1/2 -255
11/2- -661
5/2+ -1654
121
7/2+ -2434
Zr
135
40 81 131
133 Te
Xe
50Sn81 52 81 54 81
137
56
1/2+ -194
0
1/2+ -110
11/2- -754 11/2- -757 11/2- -754 11/2 -722
139
141
Ba 81 58 Ce 81 60 Nd 81
143
62
145
Sm81 Gd
64
81
Binding of various layers of neutrons by pf shell protons.
pf proton core
80
40
90
40
96
40
Zr 40
pf neutron core
Zr 50
Zr 56
10 g9/2 neutrons
Adding 10 g9/2 protons
132
50
Sn 82
6 d5/2 neutrons
little neutron skin
110
40
Zr 70
122
40
Zr 82
8 g7/2 neutrons
BIG neutron skin
12 h11/2 neutrons
140
58
Ce 82
Adding 8 g7/2 protons
In other words, it takes ALL 18 g9/2 protons to fully
bind the 12 h11/2 neutrons.
N = 81 hole nomalized to the
d-3/2 hole in Sn-131.
3/2+
0
11/2 -50(75)
1/2+ -331
3/2+
3/2+
0
1/2+ -308
0 3/2+
0
1/2+ -288 1/2+ -283
11/2- -526
11/2- -661
11/2- -334
3/2+
0
3/2+
0
3/2+
0
1/2+ -255
1/2+ -194
1/2+ -110
11/2- -754
11/2- -757
11/2- -754
1/2+ +27
1/2+ +72
1/2+ +111
3/2+
3/2+
3/2+
0
11/2- -722
(749)
5/2+ -1654
7/2+ -2434
In this region as Z increases from 50 to 58,
the protons are filling the g 7/2 orbitals, and
then from 58 to 64 the protons are filling
the d5/2 orbitals.
135
131
133 Te
Sn
50
81 52
81
137
Xe 81 56 Ba 81
54
139
Ce 81
58
141
Nd 81
60
0
11/2- -679
(751)
0
11/2- -631
(742)
Starting at Z = 65, the
protons are filling
the s1/2, d3/2, h11/2
orbitals.
143
145
Sm
Gd
62
81
64
147
81
Dy 81
66
149
68
The h-11/2 neutrons seem insensitive to h-11/2 protons!!
Er
81
13/2+
2625
5/22004
13/2+
2713
C2S =4
2+
1971
9/21915
1/21656
9/21561
h9/2
2+ 5/22+
9/2 1313 9/212801246
1220
5/21/21083
1/2986
C2S =3
9/29/2
1774
9/21739 2+ 5/21619 +
2
2+
- 1660 1/25/2
13/2+1596
5/2-1575
+
2
9/25/2+
9/2
13/2
1423
1436
1407
9/2
C2S =6
1/2
9/21355
1306
1283
1/213/2+
1137
13/2+
1/2
1423
1082
C2S =6
3/2854
3/2658
3/2601
g7/2 protons
7/2- 0 0+ 7/2133
Sn
134
Te 135Te
1/22+ 9/21677
2+
9/2- 2+
1578
9/2- 2+
1531
1513
9/21397
9/2-
0+ 7/2-
0+ 7/2-
0+ 7/2-
0+ 7/2-
0+ 7/2-
138
140
142
144
Ce 141Ce
13/2+
3/2984
9/2801
d5/2 protons
Ba 139Ba
1/213/2+
1091
9/213/2+
3/21035
3/21152
13/2+
9/2567
136
Xe 137Xe
1846
3/2893
3/2742
3/2662
3/2627
1/2-
Nd 143Nd
Sm 145Sm
h11/2 protons
0+ 7/2146
Gd 147Gd
N =83 ISOTONES
0+ 7/2148
Dy 149Dy
0+ 7/2-
0+ 7/2-
150
152
Er 151Er
Yb 153Yb
0+
154
Hf
Acta Physica Pol. B 27, 475 (1996).
i13/2
1/2-
5/2-
p1/2
2340
5/2-
f5/2
1770
3/2-
p3/2 1442
13/2+
i13/2
7/2-
f7/2
i
13/2+ 13/2 2694(200)
Sn = 2455 (45)
708
0
f5/2
9/2-
p1/2
h9/2
3/2-
p3/2
1/2-
7/2-
f7/2
2004
h9/2
-1073
207
82 Pb 125
f5/2
2694
2004
1656
p1/2
1656
1561
h9/2
1561
854
p3/2
h9/2
2561
f5/2
1920
p1/2
946
854
i13/2
5000
h9/2
3600
152
50 Sn102
f5/2
0
f7/2
0
normal l2
p3/2
154
f7/2
0
0.7 l2
1850
146
Sn 96
50
p1/2
133
Sn 83
50
9/2-
i13/2
3800
f7/2
250
0
0.4 l2
p3/2
-500
9/2+ 3009
9/2+ - 5/2- gap = ~2200 keV
9/2+ - 5/2- gap = ~1500 keV
9/2+ - 5/2- gap •2 000 keV
+
9/2 1007
9/2+ 0
9/2+ - 5/2- gap =1700 keV 1/2 588
9/2+ 6000
5/2- 6000 5/2- 3991
New Shell Gap
at N = 34???
1/2- 0
1/2- 1112
5/2- 769 5/2- -694
3/2- -1140
3/2- 0
67
57
Ni
Ni
28
39
28
29
3/2- 1095
5/2- 1451
89
40
Zr
49
1/2- 2023
W. B. Walters, Seyssins, France, AIP Conference Series 447, 196 (1998 ).
1/2- 1000
7/2-
0
3/249
0
20
29
Ca
7/2- -2500 7/2- -5500
7/2- -6500
7/2- -7500
3/2- -1000
43
Si
14
29
Possible double magic nuclide
48Si
34
Projected
Monopole shift of the p3/2 and p1/2 neutron orbitals
with changing nuclear size and N/Z ratio.
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.
Deformation changes all of that for Sr and Zr by bringing g9/2 protons
up from below Z = 40
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.
Notice that there IS a valley at A = 180…the N = 126 shell works.
Heaviest known yrast structures
A = 112
N = 1.6 Z
A = 124
Sn
In
Cd
g 9/2
Ag
Pd
Rh
r process
path
Ru
Tc
Mo
N=2Z
Nb
Zr
Y

p1/2
Sr
Rb
Kr
p 3/2
Br
Se
As
f 5/2
Ge
Ga
Zn
Cu 
Ni 

N 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
d 5/2
s1/2
d 3/2
h 11/2