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The 1983 atomic mass evaluation
Nuclear Physics A432 (1985) 140-184 0 North-Holland Publishing Company
THE 1983 ATOMIC MASS EVALUATION * (III). Systematics of separation and decay energies K. BOS National Institute of Nuclear Physics and High-Energy Physics, NIKHEFAmsterdam, The Netherlands
H, PO Box 4I882, 1009 DB
G. AUDI L.aboraroire RenC Bernas du CSNSM, BXmenllO8,
91406 Orsay, France
A.H. WAPSTRA National Insiitute of Nuclear Physics and High-Energy Physics, NIKHEF- K, PO Box 4395, 1009 AJ Amsterdam and University of Technology, De& The Netherlandr Received
13 July 1984
Abstract: This third paper in a series of four presents graphs of separation energies of two protons and of two neutrons as functions of 2 and N respectively, and of n-, /3- and P/?-decay energies as functions of N, A and A respectively.
Introduction The graphs shown
presented
in the figures
here supersede
have been
earlier
derived
from
systematics least-squares
‘). Most of the values adjustment
of many
experimental data. For the sake of completeness, however, some data have been added, which were estimated during the preparation of the graphs themselves. This was done by demanding that all five graphs should be as smooth as possible, except where they are expected to show the effects of shell closures or nuclear deformations. In addition to the rather severe constraints imposed by the requirement of simultaneous smoothness of all five systematics, many further constraints resulted from knowledge of reaction or decay energies in the regions where these estimates were made. These regions and these constraints are shown in fig. 2 of part I. Two * This work has been undertaken with the encouragement of the IUPAP Commission Nomenclature, Atomic Masses and Fundamental Constants (SUN-AMCO).
140
on Symbols,
Units,
K. Bos et al. / Atomic mass evaluation (III)
141
kinds of constraints are present. In some cases the masses of (2, A) and (2, A + 4) are known but not the mass of (Z, A + 2). Then, the values of S,,( A + 2) and S,,( A + 4) cannot both be chosen freely from systematics; their sum is known. In other cases, the mass differences between several nuclides (A + 4n, Z -t 2n) are known from a-decays and also those of (A - 2 + 4n, Z + 2n). Then, the differences between several successive S,,( A + 4n, Z + 2n) are known. Similar situations exist for two or three successive .!$,‘s or Q,‘s. Sufficient values have been estimated so that every nucleus for which there is any experimental Q-value is connected to the main group of primary nuclei. In addition, an estimated value is included for any nucleus if it is between two experimentally studied nuclei on a line defined by either Z = constant, N - Z = constant, or, in a few cases, N = constant. N-Z:
MeV ,
w ,+--
p.9_Q-.os 0,
Too-”
Jr
Hf o-----+
. q-
1
160
1 -“‘____“_‘-.‘___y~
I
’
&
L
170 A-
180
Fig. A. Deuteron pairing energy (eq. .(l)) plotted as a function of A for constant values of (N - Z) indicated at the lines. For easier distinction, lines for successive values of (N - Z) have been drawn and dotted alternatively. Not strictly experimental values have been indicated by open circles linked by lighter lines. In order not to overload the figure, element symbols have been given only along the borders.
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K. Bos et al. / Atomic maw evaluation (III)
The above selection of graphs was chosen since all but Q- are not seriously influenced by the even-odd straggling due to neutron and proton pairing energies: S,,, SzP, Q, and Q-- connect points on the same sheet of the fourfold binding energy surface (in a plot of binding energy versus Z and N). This, though, only guarantees smooth plots if the four sheets are nearly parallel. As a function of A, this is indeed the case, as has been known for a long time. Fig. A shows, though, that the distance between the even-even sheet and odd-odd one varies rather drastically as a function of the neutron excess (N - Z). The quantity plotted is &=a(-1)“+‘{M(_4+2,Z+1)-3M(A,Z)+3M(A-2,Z-1) -M(A
-4,
z-2)},
(1)
which is a second-order approximation of the distance between the even-even and odd-odd binding-energy sheets. In this respect we would like to mention that Vogel, Jonson and Hansen *) recently suggested representing the pairing energies by
which may indeed be a more In view of this point, one which only data on the same inclined to think this only two-proton binding energies
useful approximation than earlier formulae. may consider replacing the figs. l-24 by new ones in binding-energy subsheet are connected by lines. We are important for detailed studies such as that of the around the semi-magic number Z = 64 presented by
Blomqvist et al. 3). They subtract also a linear function of Z and N before plotting, in order to show details more clearly. They show only points for even-even nuclides. As an illustration, we give for this region in fig. B a similar plot for all data, drawn in the way suggested
above. The data indeed
N is close to 82 (thus, around closures.
suggest some extra stability
‘ZiGd) but the effect is far smaller
at Z = 64 if
than at major shell
References 1) K. Bos and A.H. Wapstra, At. Nucl. Data Tables 19 (1977) 277, and references therein 2) P. Vogel, B. Jonson and P.G. Hansen, Phys. Lett. 139B (1984) 227 3) J. Blomqvist, P. Kleinheinz and P.J. Daly, Z. Phys. A312 (1983) 27
144
K. Bos et al. / Atomic mms evaluation (III)
Figures Figs. l-6.
2n separation
Figs. Figs. Figs. Figs.
2p separation energies. a-decay energies. &?-decay energies. P-decay energies.
7-10. 11-16. 17-24. 25-40.
energies.
Mass numbers and (or) element indications are indicated only along the borders of the ‘graphs; those for the intermediate points must be derived by enumeration. Open circles represent values estimated from systematic trends, points experimental values; error bars are given only when the error exceeds 40 keV. Lines connect points for isotopes (S,,, Q,, Q--, connected to open points.
Q-)
or isotones
(S2r,
Q-- ,Q-); the lines are dotted if
0
10
\o,,, BE
bn(7 a
15
C FIG.
I 20
25
TWO NEUTRON SEPRRATION N=9 TO 35
ENERGIES 30
NEUTRON
NUMBER
35
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20
20
\
22
22
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24
211
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26
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17 BE ~
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THE 1983 ATOMIC MASS EVALUATION * (III). Systematics of separation and decay energies K. BOS National Institute of Nuclear Physics and High-Energy Physics, NIKHEFAmsterdam, The Netherlands
H, PO Box 4I882, 1009 DB
G. AUDI L.aboraroire RenC Bernas du CSNSM, BXmenllO8,
91406 Orsay, France
A.H. WAPSTRA National Insiitute of Nuclear Physics and High-Energy Physics, NIKHEF- K, PO Box 4395, 1009 AJ Amsterdam and University of Technology, De& The Netherlandr Received
13 July 1984
Abstract: This third paper in a series of four presents graphs of separation energies of two protons and of two neutrons as functions of 2 and N respectively, and of n-, /3- and P/?-decay energies as functions of N, A and A respectively.
Introduction The graphs shown
presented
in the figures
here supersede
have been
earlier
derived
from
systematics least-squares
‘). Most of the values adjustment
of many
experimental data. For the sake of completeness, however, some data have been added, which were estimated during the preparation of the graphs themselves. This was done by demanding that all five graphs should be as smooth as possible, except where they are expected to show the effects of shell closures or nuclear deformations. In addition to the rather severe constraints imposed by the requirement of simultaneous smoothness of all five systematics, many further constraints resulted from knowledge of reaction or decay energies in the regions where these estimates were made. These regions and these constraints are shown in fig. 2 of part I. Two * This work has been undertaken with the encouragement of the IUPAP Commission Nomenclature, Atomic Masses and Fundamental Constants (SUN-AMCO).
140
on Symbols,
Units,
K. Bos et al. / Atomic mass evaluation (III)
141
kinds of constraints are present. In some cases the masses of (2, A) and (2, A + 4) are known but not the mass of (Z, A + 2). Then, the values of S,,( A + 2) and S,,( A + 4) cannot both be chosen freely from systematics; their sum is known. In other cases, the mass differences between several nuclides (A + 4n, Z -t 2n) are known from a-decays and also those of (A - 2 + 4n, Z + 2n). Then, the differences between several successive S,,( A + 4n, Z + 2n) are known. Similar situations exist for two or three successive .!$,‘s or Q,‘s. Sufficient values have been estimated so that every nucleus for which there is any experimental Q-value is connected to the main group of primary nuclei. In addition, an estimated value is included for any nucleus if it is between two experimentally studied nuclei on a line defined by either Z = constant, N - Z = constant, or, in a few cases, N = constant. N-Z:
MeV ,
w ,+--
p.9_Q-.os 0,
Too-”
Jr
Hf o-----+
. q-
1
160
1 -“‘____“_‘-.‘___y~
I
’
&
L
170 A-
180
Fig. A. Deuteron pairing energy (eq. .(l)) plotted as a function of A for constant values of (N - Z) indicated at the lines. For easier distinction, lines for successive values of (N - Z) have been drawn and dotted alternatively. Not strictly experimental values have been indicated by open circles linked by lighter lines. In order not to overload the figure, element symbols have been given only along the borders.
Y
-3EJq3
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-2 s9
09
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aql
OL
‘$f%~
143
K. Bos et al. / Atomic maw evaluation (III)
The above selection of graphs was chosen since all but Q- are not seriously influenced by the even-odd straggling due to neutron and proton pairing energies: S,,, SzP, Q, and Q-- connect points on the same sheet of the fourfold binding energy surface (in a plot of binding energy versus Z and N). This, though, only guarantees smooth plots if the four sheets are nearly parallel. As a function of A, this is indeed the case, as has been known for a long time. Fig. A shows, though, that the distance between the even-even sheet and odd-odd one varies rather drastically as a function of the neutron excess (N - Z). The quantity plotted is &=a(-1)“+‘{M(_4+2,Z+1)-3M(A,Z)+3M(A-2,Z-1) -M(A
-4,
z-2)},
(1)
which is a second-order approximation of the distance between the even-even and odd-odd binding-energy sheets. In this respect we would like to mention that Vogel, Jonson and Hansen *) recently suggested representing the pairing energies by
which may indeed be a more In view of this point, one which only data on the same inclined to think this only two-proton binding energies
useful approximation than earlier formulae. may consider replacing the figs. l-24 by new ones in binding-energy subsheet are connected by lines. We are important for detailed studies such as that of the around the semi-magic number Z = 64 presented by
Blomqvist et al. 3). They subtract also a linear function of Z and N before plotting, in order to show details more clearly. They show only points for even-even nuclides. As an illustration, we give for this region in fig. B a similar plot for all data, drawn in the way suggested
above. The data indeed
N is close to 82 (thus, around closures.
suggest some extra stability
‘ZiGd) but the effect is far smaller
at Z = 64 if
than at major shell
References 1) K. Bos and A.H. Wapstra, At. Nucl. Data Tables 19 (1977) 277, and references therein 2) P. Vogel, B. Jonson and P.G. Hansen, Phys. Lett. 139B (1984) 227 3) J. Blomqvist, P. Kleinheinz and P.J. Daly, Z. Phys. A312 (1983) 27
144
K. Bos et al. / Atomic mms evaluation (III)
Figures Figs. l-6.
2n separation
Figs. Figs. Figs. Figs.
2p separation energies. a-decay energies. &?-decay energies. P-decay energies.
7-10. 11-16. 17-24. 25-40.
energies.
Mass numbers and (or) element indications are indicated only along the borders of the ‘graphs; those for the intermediate points must be derived by enumeration. Open circles represent values estimated from systematic trends, points experimental values; error bars are given only when the error exceeds 40 keV. Lines connect points for isotopes (S,,, Q,, Q--, connected to open points.
Q-)
or isotones
(S2r,
Q-- ,Q-); the lines are dotted if
0
10
\o,,, BE
bn(7 a
15
C FIG.
I 20
25
TWO NEUTRON SEPRRATION N=9 TO 35
ENERGIES 30
NEUTRON
NUMBER
35
N
20
20
\
22
22
cu
24
211
\
26
26
.\
28
28
17 BE ~
30
30
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32
32
0
2
la
34
311
h
A
,B
146
K. Bos et al. / Atomic mass evaluation (III)
-
K. Bos et al. / Atomic mass evaluation (III)
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