Energy levels of Bip210 and Pop210 and the shellmodel residual force

Nuclear Physws 61 (1965) 173--176, (~) North-Holland Pubhshmg Co, Amsterdam o

Not to be reproduced by p h o t o p r m t or mJcroftlm w i t h o u t wrttten permlsston from the p u b h s h e r

ERRATA A. K. Sen G u p t a and D M. Van Patter, Studies of the low-lying energy levels of Zn 64 and Zn ~6, Nuclear Physics 50 (1964) 17. Page 18, hne 9, should read "applied to extract information" Page 24, fig. 3, the extreme right-hand column for ~-ray energies, should read 1.62 1.33 0.91 1.80 0.81 0 99

Y E. K l m and J. O. Rasmussen, Energy levels of BI2x° and P o 21° and the shellmodel residual force, Nuclear Physics 47 (1963) 184. The expression for
IJm) = I(ls)jm) = ~(lmlsmsljm)llmism,). Slight changes must be made in tables 5 and 6 due to this phase-factor error that ' Is odd The affects off-diagonal, central-force matrix elements when Jl +J2 4 -Jl' - t -J2 corrected tables 5 and 6 are presented. In this same convention, the expression (,jlj2JMIT~ lx)K T~IY)r[j~j~JM) appearing on p. 190 should be multiplied by ( - 1 ) s'+12+J'l+i2. Also in the same expression, the lower case k appearing in the 6 j-symbol should read as a capital K The calculations were made correctly, however. All elgenvalue changes are so small that they would be imperceptible in figs 8 and 9 and do not alter any conclusions The other changes resulting from these corrected wave functions were negligible except for the value of ~ which is now - 0 91 instead o f - 0 63. This new value of is consistent with both Fujlta's and Spector's limits for A typographical error not affecting any calculations Is m the expression for (alVC(r12)[a ') on p. 188. The smglet projection operator P, should be inserted in the matrix element of the second line of this expression, l e. (alUcE(rl2)P~la ')

173

259 568 800 392 471

136 683 775 386 531 871

J=4 --0 0 0 I I I

9928 0295 0187 0951 0227

0 9948 - - 0 0625 0 0167 - - 0 0730 0 0264 - - 0 0162

0 0 --0 --0 --0

0 9722 - - 0 1696 0 0278 0 1577 0 0076

=2 - 0 313 0 533 0 700 1017 I 358

J = 3 --0 0 0 l l

0 9689 0 1269 0 1827

1 - - 0 617 0 091 0 548

0 9999

J = 0 - - 0 573

J=

h,g i

(MeV)

Eigenvalues

1082 9055 1813 2654 2508

0 0 --0 --0 0 0

0609 9376 3166 0149 1161 0438

- - 0 0438 0 8887 --04424 - - 0 0663 - - 0 0784

0 0 0 0 0

- - 0 2192 0 7029 0 6597

h~l~

00045 0 3185 0 9469 00013 --00003 0 0175

00098 04466 0 8914 0 0611 - 0 0221

- - 0 0330 - - 0 1514 0 9769 - - 0 1384 00055

00463 0 6952 - - 0 7045

fig|

00416 - - 0 0334 0 0144 0 8420 0 4790 - - 0 2300

0 0613 --00087 - - 0 0617 0 8525 - - 0 4959

0 1058 00015 - - 0 0969 - - 0 6715 0 7198

h~d~

TABLE 5

--0 --0 0 --0 0 0

0 0 --0 0 0

0605 1021 0343 4628 8673 0875

0631 0845 0557 4907 8603

- - 0 1706 - - 0 3488 0 0291 06402 06470

f;ll/

0 0246 --00486 --00002 0 2192 0 0364 0 9529

h|s I

00072 - - 0 0124 0 0264 00041 - - 0 0134 - - 0 0245

0 0223 0 0299 00018 0 0100 0 0305

00007 --00472 0 0280 0 0100 --00030

00051 0 0787 0 0639

f~d~

Eigenfunct~ons

Calculated elgenfunctlons for Bi sl°

0 0269 0 0202 --00070 --0 IIll - - 0 0502 0 0957

--00467 0 0177 00004 - - 0 0430 00406

0 0386 0 0619 --00012 - - 0 1499 - - 0 0144

- - 0 1034 0 0155 - - 0 0262

h~g~

0 0180 - - 0 0219 --00089 0 1009 --00039 0 1362

- - 0 0344 00064 00474 - - 0 1080 00498

hid ]

0 0108 --00090 --00026 00063 - - 0 0106 - - 0 0121

0 0191 0 0148 --00067 0 0184 0 0316

~s,~

0148 0314 0100 0329 0150

--00027 - - 0 0223 - - 0 0249 - - 0 0251 00044 - - 0 0231

0 0 --0 0 0

--00071 - - 0 0172 --00286 0 0447 - - 0 0043

- - 0 0162 - - 0 0097 0 1744

-- 0 0099

f~,g~,

0139 0204 0163 0131 0117

--00068 --00008 --00054 --00089 00089 - - 0 0003

0 0142 0 0160 --00060 0 0172 0 0225

--0 0 --0 0 0

f~,d I

0 9888 - 0 1312 - 0 0621 0 0186

0 9999 --00083 00019

J = 9 - - 0 309 0 749 1 327

0 9961 00023 -00033 - 0 0857 - 0 0147

0 9957 - 0 0715 0 0229 - 0 0372 0 0227

0 9962 o 0135 - 0 0041 - 0 0746 - 0 0220 - 0 0253

h|g|

- 0 063 0 345 0 670 1 600

J=8

- 0 220 0 705 0 857 1402 1 493

J=7

- 0 085 0642 0 761 1 481 l 574

J=6

- 0 206 0 652 0 821 l 417 1 503 1 964

r=5

(MeV)

Elgenvalucs

00084 0 9931 - - 0 1173

0 1103 0 4212 0 8978 0 0618

-00061 0 9821 - 0 1670 - 0 0297 - 0 0754

0 0700 0 8095 - 0 5764 -00030 0 0783

- 0 0189 0 9566 - 0 2775 - 0 0389 - 0 0693 - 0 0135

h~J~

0 0919 0 8969 - 0 4325 0 0062

00078 0 1653 0 9829 0 0585 - 0 0297

0 0220 0 5776 0 8149 - 0 0170 0 0042

00052 0 2777 0 9576 0 0559 - 0 0287 o 0313

f~g~

0 0 --0 0 --0

0 --0 0 0 0 0833 0146 0642 9911 0673

0216 0117 0260 9240 3516

0 0588 00048 - - 0 0562 0 9483 - - 0 2151 - - 0 2105

h~d i

0214 0285 0485 9895

0210 0786 0105 0667 9927

0356 0643 0350 3393 9290

--00010 0 1173 0 9931

--0 --0 --0 0

0 0 0 0 0

--0 --0 0 --0 0

0 0381 0 0758 --00073 0 2187 0 9699 00026

f~¥

h~sj

0 0344 00062 - - 0 0450 0 1918 --00445 0 9693

I

(continued)

00097 00022 0 0277 0 0151 - - 0 0310

--00023 0 0149 00041 --00029 0 0251 - - 0 0229

f½dt

E~gcnfunctlons

TABLE 5

0202 0074 0012 0391 0390

0282 0152 0109 0886 0677

0 0357 00073 • 0 0285 --0 1293

-- 0 0 0 --0 0

0 0 --0 0 --0

- - 0 0235 0 0115 00017 - - 0 0395 00426 - - 0 0641

h|g;

0 0240 - - 0 0267 00099 0 1096 - - 0 0342

- - 0 0205 --00020 0 0204 --00638 0 0211 --00982

h|d|

fis~

-- 0 0 0 0 0

0006 0406 0416 0046 0427

--00020 - - 0 0269 - - 0 0174 0 0101 00044

00022 0 0322 0 0181 0 0187 0 0257 00095

f~g~

00064 0 0186 00012 00079 0 0367 --00043

f~d|

176

ERRATA TABLE 6 Ca~ulated elgenfuncttonsfor the even-parltysta~sm Eigenvalue

Po zl°

E~genfunct~ons

(MeV)

hj ht

h t ft

ft ft

l~ I

J=O --1 597 1 016 2 718

0 8845 - - 0 3697 0 2844

J=2 - - 0 374 0 957 1 519 2 904

0 9890 00489 --00972 0 1000

--00422 0 9978 00400 - - 0 0311

0 --0 0 0

0875 0325 9894 1114

--0 0 --0 0

1113 0302 1004 9882

J=4 - - 0 168 0 893 1 664 3 052

0 9958 0 0552 --00470 0 0550

--0 0 0 --0

0523 9977 0258 0333

00449 - - 0 0214 0 9969 0 0614

--0 0 --0 0

0595 0317 0579 9960

0 0 --0 0

--0 0 0 --0

0637 9971 0182 0367

0 0257 - - 0 0152

- - 0 0392 0 0349 - - 0 0359 0 9980

J=6 - - 0 086 0 827 1 742 3 119 J=8 - - 0 032 0 630 3 161

9969 0655 0260 0359

0 9940 0 1068 0 0234

0 3032 0 9190 0 2517

- - 0 1056 0 9933 --00471

0 9989

0 0374

- - 0 3544 - - 0 1364 0 9250

- - 0 0283 0 0443 0 9986