Nuclear Masses Far from Stability - American Chemical Society

18 Nuclear Masses Far from Stability Interplay of Theory and Experiment

P. E. Haustein

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Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973 Mass models seek, by a variety of theoretical approaches, to reproduce the measured mass surface and to predict unmeasured masses beyond i t . Subsequent measurements of these predicted nuclear masses permit an assessment of the quality of the mass predictions from the various models. Since the last comprehensive revision of the mass predictions (in the mid-to-late 1970's) over 300 new masses have been reported. Global analyses of these data have been performed by several numerical and graphical methods. These have identified both the strengths and weaknesses of the models. In some cases failures in individual models are distinctly apparent when the new mass data are plotted as functions of one or more selected physical parameters. Several examples will be given. Future theoretical efforts will also be discussed. I.

Introduction

À continuing e f f o r t among experimentalists who study n u c l e i f a r from beta s t a b i l i t y i s the measurement of the atomic mass s u r f a c e . As a manifestation of the nuclear force and the nuclear many body system, atomic masses s i g n a l important features of nuclear s t r u c t u r e on both a macroscopic and microscopic s c a l e . I t has thus been a challenge to nuclear t h e o r i s t s to devise models which can reproduce the measured mass surface and to p r e d i c t s u c c e s s f u l l y the masses of new isotopes. Both the measured mass surface and that beyond i t which can be predicted by these models serve as important input to a v a r i e t y of fundamental and applied problems, e.g., nucleosynthesis c a l c u l a t i o n s , p r e d i c t i o n s of decay modes of e x o t i c n u c l e i far from s t a b i l i t y , nuclear d e - e x c i t a t i o n by p a r t i c l e evaporation, decay heat simulations, e t c . Well determined masses of n u c l e i which l i e f a r from beta s t a b i l i t y can provide very s e n s i t i v e t e s t s of atomic mass models. While a s i n g l e new mass measurement from one p r e v i o u s l y uncharacterized isotope c a r r i e s with i t only l i m i t e d information about the q u a l i t y of mass p r e d i c t i o n s from the models, important trends frequently become evident across i s o t o p i c sequences or when g l o b a l comparisons of many new masses are made against the various mass models. I t i s i n t h i s context that a comprehensive and c r i t i c a l assessment of the p r e d i c t i v e properties of atomic mass models i s presented with the aim of i d e n t i f y i n g both the successes and f a i l u r e s i n the models. A summary of a p o r t i o n of t h i s e f f o r t has been published e a r l i e r [HAU84]· 0097-6156/ 86/0324-0126S06.00/0 © 1986 American Chemical Society

Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

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Nuclear Masses Far from Stability

I I . New Masses, A n a l y s i s Methods, and Global Comparisons The l a s t comprehensive update of the atomic mass p r e d i c t i o n s from nine d i f f e r e n t models was published i n 1976 [MAR76]· A d d i t i o n a l p r e d i c t i o n s from other models appeared i n the l a t e 1970's and early 1980's [MON78], [M0L81], [UN082]. In each case, one of the atomic mass evaluations p e r i o d i c a l l y provided by Wapstra [MAR76], [WAP77], [WAP84], served as the experimentally determined mass data base on which the adjustable parameters of the models were determined. Since the 1975 Wapstra evaluation (which was used i n the formulation of many of the models published i n 1976) over 300 new mass measurements have been made. An examination of where these new measurements occur i n the Chart of Nuclides reveals that they are d i s t r i b u t e d among almost a l l the elements at t h e i r most neutron-rich or neutron-deficient isotopes. E s p e c i a l l y long i s o t o p i c sequences of new masses occur i n the Na, Rb, and Cs n u c l e i and i n alpha decay chains which o r i g i n a t e from H g and Hg. It i s quite i n s t r u c t i v e to compare these new measurements (which l i e outside the data bases a v a i l a b l e at the time the various mass models were formulated) with p r e d i c t i o n s from the models. For such comparisons i t i s convenient to define Δ • Predicted Mass - Measured Mass. Δ > 0 thus denotes cases where the binding energy has been predicted to be too low and conversely, Δ < 0 corresponds to a p r e d i c t i o n of too much nuclear binding. Table 1 summarizes average and root-mean-square deviations f o r twelve models. 1 7 6

Table 1. Model

M GHT SH MN Β BLM LZ UY CK JGK MS JE +

+

+

+

1 7 8

Average and Root-Mean-Square Data Base Used 1971 1975 1971 1977 1971 1971 1975 1975 1975 1975 1975 1975

1

4

Old Masses" " " RMS-Δ 209 20 -6 -4 -459 1984 7 0 5 6 -7 0

1327 718 718 835 1506 2747 276 393 312 212 159 363

Deviations ( a l l energies i n keV) New Masses

New

Masses RMS-Δ

270 276 257 213 121 146 268 219 258 271 267 239

-551 -478 -195 279 -768 1991 87 110 186 219 -6 24

1566 1096 954 970 1772 3125 589 1100 1314 1361 695 952

RMS Ratio 1.18 1.53 1.33 1.16 1.18 1.14 2.13 2.80 4.21 6.42 4.37 2.62

M = Myers, GHT « Groote et a l . , SH - Seeger & Howard, MN = Mo'ller & Nix, Β = Bauer, BLM = Beiner et a l . , LZ = L i r a n & Zeldes, UY = Uno & Yamada ( l i n e a r s h e l l s ) , CK - Comay & Kelson, JGK » Ja'necke, Garvey-Kelson, MS - Monahan & Serduke, JE - Ja'necke & Eynon. R e l a t i v e to the 1975 Wapstra masses.

Several s i g n i f i c a n t trends are apparent. < ^ values f o r the 1975 masses are quite small, t y p i c a l l y a few k i l o v o l t s except f o r those models


128

NUCLEI OFF THE LINE OF STABILITY

which used the 1971 Wapstra masses. RMS-Δ values range from 159 to 2747 keV. This spread i s a r e f l e c t i o n of the degree of conformation of the c a l c u l a t e d mass surface to the measured one afforded, i n those models with smaller RMS-Δ values, by the use of i n c r e a s i n g l y l a r g e r numbers of adjustable parameters. When g l o b a l comparisons are made f o r a l l the models to the new masses (up to 276 n u c l e i ) reported since 1975-77 one notes that approximately h a l f of the models d i s p l a y net p o s i t i v e values and the remainder net negative values. RMS-Δ values f o r the new masses reveal that a l l models show poorer f i t s to these masses than to the 1975 or '77 data base. The l a s t column l i s t s the r a t i o of the rms-deviations of the new masses to the o l d ones. The more "fundamental" models (e.g., l i q u i d drop, d r o p l e t , simple s h e l l ) have l a r g e r RMS-Δ deviations when compared to the old masses than the models based on mass r e l a t i o n s or complicated s h e l l c o r r e c t i o n s . However the comparison also reveals that these simpler approaches show s u b s t a n t i a l l y smaller enlargement of rms d e v i a t i o n s ; models based on mass r e l a t i o n s (CK, JGK, and MS) e x h i b i t l a r g e r RMS r a t i o s , up to f a c t o r s of 6.4, which r e s u l t from p r o g r e s s i v e l y poorer p r e d i c t i o n s f o r n u c l e i e s p e c i a l l y f a r from s t a b i l i t y . III.

A n a l y s i s of Selected I n d i v i d u a l Models

A. Seeger and Howard: Figure 1 d i s p l a y s Δ values for new masses as a f u n c t i o n of neutron number f o r t h i s model (semiempirical l i q u i d drop plus s h e l l c o r r e c t i o n s ) . The s o l i d l i n e s pass through sets of points where Δ

20

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60 80 100 120 NEUTRON NUMBER

140

Delta values of new masses as a function of neutron number f o r the model f o r Seeger and Howard.


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values are linear with neutron number N. The more obvious of these i s the rapidly f a l l i n g trend which begins near Ν = 114 and continues to Ν • 126, followed by a reversal that extends to Ν • 150. Another trend starts for points with Ν • 82 and extends for approximately ten neutron numbers. The correlation of these effects with neutron shell closures at Ν = 82 and 126 may be understood by examination of the treatment of the microscopic shell corrections i n the Seeger and Howard model [SEE75]. Without invoking an ad hoc enlargement of the Ν = 126 shell gap by 3 MeV (which tapered smoothly and symmetrically to zero at Ν - 108 and Ν = 144) i t was not possible to obtain simultaneously the proper single particle level ordering and a good f i t to the known (1971) mass surface. The Ν • 82 gap i s affected to second order by this prescription. While an optimized f i t to the 1971 masses was obtained in this way, the trend in the predictions of masses of nearly a l l new isostopes (since 1971) with Ν = 114 to 150 and some new masses for isotopes with Ν = 82 to 92 i s clear evidence that the procedure described above w i l l not work satisfactorily for these nuclei which l i e further from s t a b i l i t y . B. Ja'necke, Garvey-Kelson: The value of 6.42 in the RMS Ratio column in Table 1 for this model i s a result of a small number of very poorly predicted masses for nuclei quite far from s t a b i l i t y . Closer to s t a b i l i t y this model (and similar ones, e.g., CK and MS) provide excellent predictions with Δ values usually within ±1.5 MeV. A useful way to i l l u s t r a t e this feature in these models i s by plotting Δ values as a function of how far each isotope i s from the valley of beta s t a b i l i t y . For this purpose, the quantity N - Z - (0.4A )/(200 + A) gives the difference in neutron numbers of the isotope of interest and that of the isotope nearest the s t a b i l i t y line of the same element. Positive values of this quantity correspond to neutron-rich nuclei, negative values to proton-rich nuclei, and values near zero represent nuclei close to the s t a b i l i t y l i n e . Figure 2 displays Δ values versus number of neutrons from s t a b i l i t y for this model. Many points cluster about the dashed horizontal Δ = 0 line but there i s a clear trend that shows that proton-rich nuclei are not bound enough and neutron-rich nuclei are too well bound. Use of this model (and the others of similar type) for calculations of r-process nucleosynthesis w i l l therefore introduce a strong bias that results from the prediction of the location of the neutron drip line too close to s t a b i l i t y . As shown here the trend i s approxiimately proportional to T and i s a reflection of need for correction terms [JAN84] in the transverse Garvey-Kelson mass relationship on which these models are based. 2

3

z

C. Ja'necke and Eynon: This model, which involves the solution of inhomogeneous third order partial difference equations, represents one approach that aims to correct the deficiencies of type noted above i n models that employ (homogeneous) mass relations. In particular, the introduction of an inhomogeneous term i s meant to account for variations i n the effective neutron-proton residual interaction as a function of nucléon number and neutron excess. It i s therefore instructive to compare the quality of mass predictions from this model to those which derive their mass predictions from solutions of homogeneous partial difference equations. Figure 3 shows a plot of Δ values versus neutrons from s t a b i l i t y for the Ja'necke and Eynon model. Two features are immediately apparent: (1) the largest Δ values are considerably reduced — note the


NUCLEI OFF THE LINE OF STABILITY

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Delta values f o r new masses as a f u n c t i o n of neutrons from s t a b i l i t y f o r the model of JSnecke and Eynon.


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131

change of a f a c t o r of 2.5 i n the v e r t i c a l scale r e l a t i v e to Figure 2; and (2) points s c a t t e r more uniformly into the four quadrants of the p l o t , suggesting that the i s o s p i n dependence has been more s u c c e s s f u l l y t r e a t e d . One expects, therefore, that t h i s model would be more s u i t a b l e for use as input for nucleosynthesis c a l c u l a t i o n s or i n other a p p l i c a t i o n s r e q u i r i n g more r e l i a b l e p r e d i c t i o n s f a r o f f the s t a b i l i t y l i n e . IV.

Sunoary and Future D i r e c t i o n s

The a n a l y s i s methods described here have h i g h l i g h t e d some of the systematic features i n the p r e d i c t i v e properties of s e v e r a l of the commonly used atomic mass models. A d d i t i o n a l understanding of these features and the a v a i l a b i l i t y of many new atomic masses f o r isotopes f a r from the s t a b i l i t y l i n e w i l l serve as a basis for improving the models. The need c l e a r l y e x i s t s f o r a comprehensive r e v i s i o n and update of the mass p r e d i c t i o n s . A p r o j e c t , coordinated by the author, has been started to accomplish t h i s . I t i s expected that new sets of mass p r e d i c t i o n s from a number of groups may be a v a i l a b l e l a t e i n 1986. Acknowledgments This research was c a r r i e d out at Brookhaven National Laboratory under contract DE-AC02-76CH00016 with the U. S. Department of Energy and supported by i t s O f f i c e of High Energy and Nuclear Physics.

References [HAU84] P. Haustein, Proceedings of the 7th International Conference on Atomic Masses and Fundamental Constants (AMCO-7), 3-7 September 1984, Darmstadt-Seeheim, FRG, O. Klepper, ed., Technische Hochschule Darmstadt, 413 (1984). [JAN84] J . Jänecke, Proceedings of the 7th International Conference on Atomic Masses and Fundamental Constants (AMCO-7), 3-7 September 1984, Darmstadt-Seeheim, FRG, O. Klepper, ed., Technische Hochschule Darmstadt, 420 (1984). [MAR76] S. Maripuu, At. Data Nuc. Data Tables 17 411 (1976). [MOL81] P. Möller and J. R. Nix, At. Data Nucl. Data Tables 26 165 (1981). [MON78] J . E. Monahan and F. J . D. Serduke, Phys. Rev. C17 1196 (1978). [SEE75] P. A. Seeger and W. M. Howard, Nucl. Phys. A238 491 (1975). [UNO82] M. Uno and M. Yamada, Report INS-NUMA-40, Waseda University, Tokyo, Japan (1982). [WAP77] A. H. Wapstra and K. Bos, At. Data Nucl. Data Tables 19 175 (1977). [WAP84] A. H. Wapstra and G. Audi, Nucl. Phys. A432 1 (1984). RECEIVED May 8, 1986


Nuclear Masses Far from Stability - American Chemical Society

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