184 kev. 48 kev 124 kev. 145 kev. 230 kev. 375 kev 403 kev 31 P. 328 kev. number of D per 5 kev kev kev 1217 kev 1268 kev.

Transcription

1 NEW NUCLEAR DATA COMPILATIONS COLLECTED IN PNPI. IV. Sukhoruchkin S. I., Soroko Z. N., Sukhoruchkin D. S. Petersburg Nuclear Physics Institute 1880 Gatchina This work is a continuation of the analysis of nonstatistical effects in spacing distributions of excited states of nuclei Z=9-17 (previous parts [1,2]). We found out in Z=-17 nuclei situated at the end of 1d 5/2 shell anenhancement of tensor forces effect. At the border between 1d 5/2 and1d 3/2 subshells with spin-orbit orientations j=l+s(>) andj=l-s(<) one expects favorable conditions for tensor-force action (between nucleons with (>,<)) considered in [3]. We start with D-distribution for nucleus with one proton over the core Si and plot the adjacent distributions for different positions of maxima x kev 124 kev 145 kev 184 kev 2 kev 328 kev 375 kev 3 kev 5 kev 686 kev 778 kev 894 kev 9 kev kev 1 kev 1217 kev 1268 kev 1296 kev 1345 kev 1368 kev 14 kev 32 kev 1627 kev 1672 kev 1713 kev 1763 kev 1882 kev 19 kev kev 61 kev 2478 kev 78 kev 2444 kev 2492 kev 2789 kev 22 kev 2333 kev 29 kev 2994 kev Fig. 1. Spacing distribution in levels of for E =0-3 kev, maxima at D=686 kev, kev and triplet at 47 kev are close to 1/3ε o, 2/3ε o and 2ε o =44 kev.

2 x=686 kev 1345 kev kev x=686 kev 1345 kev kev 686 kev 1297 kev x=1345 kev kev 1672 kev x=47 kev 61 kev Fig. 2 Adjacent interval distribution in for fixed intervals x=686 kev in both directions (maximum at 1345 kev close to the doubled position), x=1345 kev and x=47 kev.

3 In spacing distribution of rational relations between values of stable intervals were found. Intervals D=686 kev, kev, the triplet at 47 kev (Fig.1) and D=95 kev (Fig.3 top) are close to ε o /3, 2ε o /3, 2ε o and 4ε o. Results of the application of AIM-method for x=686 kev (Fig.2 top, maxima at doubled energy in both directions), x=1345 kev (doublet at x/2), x=47 kev (doublet with 61 kev) and x=95 kev (Fig. 3 center, maximum at x/2) confirm a systematic character of the spectrum. Totalspacingdistributionfor 32 PispresentedinFig.4(top). MaximumatD=2314keV equalstothesumoftwoparametersδm N +ε o coincideswiththeexcitatione =2313.5keV (see Table 1 in [1]). The interval 86 kev adjacent with it (Fig.4 center) coincides with thedoubledvalueoftheparameter δm N. Anexample ofinteger relationbetween valuesof stable intervals can be seen in Fig.4(bottom). Here the stable character of observed stable interval D=274 kev is resulted in the ratio between intervals kev kev kev 38 kev 95 kev 4139 kev 4192 kev kev 5 kev x=95 kev 47 kev = (1/2) 95 kev kev 894 kev 74 kev = 2x37 kev x=38 kev Fig. 3 Adjacent interval distribution in for the fixed intervals x=95 kev (maximum at exactly one half value), x=61 kev (confirmation of adjucent excitation kev), x=513 kev (ratio 3.99=46/513 kev) and 38 kev (maximum at exactly doubled value).

4 kev 318 kev 268 kev 336 kev 698 kev 714 kev 7 kev 826 kev 892 kev 898 kev 1 kev 1168 kev 1222 kev 16 kev 1457 kev 32 P kev 17 kev 16 kev 1816 kev 19 kev 2 kev 2314 kev 2387 kev 2986 kev 32 P kev 86 kev 32 P x=2314 kev kev 1 kev 32 P x=274 kev Fig. 4. Spacing distribution in levels of 32 P for E=0-00 kev. Stable interval 2314 kev coincides with E = kev (boxed in Table 1 in the third part of this work [2]), the sum of two parameters δm N = kev and ε o =22.0 kev (nucleon mass difference and 2m e ); the maximum in its AIM-distribution (center) at 86 kev coincides with the doubled value of the parameter δm N = kev. Bottom: Adjacent interval distributionsin 32 Pfor x=274kev; maxima at 548 kev and1 kev for the ratios 548/274 kev=2.00 and 1/274 kev=4.01.

5 Table 1. Linear trend in E (kev) of levels in N=21,22 nuclei with one and three pairs of protons. Excitations forming the slope kev=4 TF are boxed ( TF =161 kev) [4-8]. (Z-14)/2 1, N=1 1, N=2 1, N=-4 3, N=1 A Z 37 S 38 S 33 S 41 Ca 41 Ca 41 Ca E, D D=322 [1] D=1944 D AIM =2912 2J π x=1944, dev. 3.6σ n( TF ) (2/3)1943=2913 n We discuss now results for and other nuclei neighbour to the 33 S considered previously [1,2]. Data on heavy sulfur isotopes 37,38 S were used [4-6] for demonstration of stability of excitations connected with tensor forces. These two nuclei have one and two neutrons in 1f 7/2 subshell (>) over the closed 1d 3/2 core (<). First excitation of these nuclei are in exact 1:2=646 kev:1292 kev relation, they coincide with 4 TF and 8 TF (Table 1 left) where the parameter 4 TF of the interaction between nucleons with (>,<) combination of spin-orbit orientation was introduced from excitations in odd Sb isotopes [1,4-7]. Stableintervalseen asamaximum inspacingdistributionin 33 Sat322keV=2 TF (central column in Table 1) is in agreement with the discussed effect in excitations of 33 S. It was noticed that excitation in 41 Ca nucleus with one valence neutron ( N=1) and three pairs of protons in 2s1d 3/2 subshell (relative to 37 S) is exactly three times the excitation in 37 S. In D-distribution of 41 Ca a stable interval 1944 kev=(12=2 6) TF was found. The application of AIM analysis to 1 intervals forming maximum at 1944 kev results in D AIM distribution with the strongest maximum at 2914 kev (129 intervals in both AIM directions, 3.6σ deviation from the mean value). It corresponds exactly to 3/2 of the x=1944 kev. This result for the border (>,<) nucleus shows the stable character (within 3-9 kev) of tensor force parameters in different Z,N regions including light nuclei 18 F, 24 Na [1] and heavy nuclei like Hf where large 1h 11/2 shell (>) starts filling up [6] kev 384 kev 3 kev 22 kev kev 1388 kev kev 1474 kev 12 kev 1965 kev 24 kev 32 S Fig. 5. D-distribution in levels of 32 S for E=0- kev, maxima are discussed in the text. 32 S 14 kev

6 Results for 32 S shows long-range correlations with the parameter 492 kev observed in 18 F situated at the beginning of this 1d 5/2 subshell. Stable interval 1965 kev coinciding with the equidistant excitations in 33 S appears together with the stable interval 1474 kev in different distributions shown in Fig.5-7. Intervals are close to 492 kev 3=1976 kev and 492 kev 4=1968 kev. In AIM method of spacing analysis usually both directions are use: plotting intervals upwards from the low-energy end of the fixed interval x and downwards from the top end of the fixed x. Stable interval D=4414 kev observed in spacing distribution for the energy region -5 kev (Fig.7 top) is close to kev=4422 kev. Intervals kev are forming AIM-triplets as it can be seen from D AIM - distributions in Fig 7 (2-nd line and center). Maximum at 4414 kev in the distribution for x=1965 kev (Fig.7 2-nd line) has a deviation from the mean value more than 4δm N and ε o could be extended with the analysis of spin values kev 32 S x=3 kev kev 32 S x=348 kev 1474 kev kev 1474 kev S x=2862 kev Fig. 6. Adjacent interval distribution in 32 S for x=3 kev, 348 kev and 2862 kev. Intervals D AIM =1965 and 1474 kev in distributions for x=3-348 kev are rational as 4/3 (1965 kev/4=491.2 kev and 1474 kev/3=491.3 kev). Intervals 1965 kev and 2862 kev in 32 S are close to excitations in 33 S at kev.

7 32 S 2986 kev 3499 kev 4414 kev 4123 kev 07 kev 4559 kev S 4414 kev 45 x=1965 kev S x=4414 kev 1474 kev 1967 kev S kev x=8 kev 336 kev 752 kev 4 kev S x=24 kev 22 kev 2487 kev Fig. 7. Top: Spacing distribution in 32 S for energies kev - 5 kev. 2-nd -bottom: Adjacent interval distribution for x=1965 kev, 4414 kev, 8 kev, 24 kev. Intervals kev are forming triplets with rational relations with the period 4414 kev/9=4.4 kev. Intervals 1965 kev and 2862 kev in 32 S are close to excitations in 33 S at kev. In the distribution for x=8 kev two the first and two the last maxima are in ratios 2/1=338/169 kev and 4:5:6=8:752:4 kev. Bottom: D=22 kev=εo.

8 kev 33 S x=11 kev kev 367 kev 736 kev 986 kev 33 S x=21 kev kev 1693 kev 93 kev 33 S x=1369 kev 1819 kev kev 33 S x=59 kev Fig. 8. Adjacent interval distribution in 33 S for x=11 kev, 21 kev, 1369 kev, 59 kev. Top: Intervals D AIM =6 kev and x=11 kev are related as 5 : 7 with the period 1936 kev:(5+7)=161.3 kev. 2-nd line: Intervals 367 kev, 736 kev and 986 kev for x=21 kev=ε o are related as 3 : 6 : 8 with the period ( kev=89 kev):(3+6+8=17)=123 kev. Center: Intervals x=1369 kev, 1439 kev, 93 kev, 1819 kev are related as 18,19,21,24. Bottom: Intervals x=59 kev and kev are related as 2 : 1 ( kev is close to ε o ).

9 InFig.8additionalresultsfor 33 S(consideredearly[1])arepresented. Rationalrelation 5:7 between 6 kev and 11 kev (Fig.8 top) as well as 3:6:8 between kev for x=ε o (Fig.8 2-nd line) confirm the distinguished character of the discussed stable character of tensor force effects with parameters 161 kev= Tf =δm N /8 [9], 1 kev=ε o /6. Table 2. Comparison of E (kev)in 32 Si (left) and 41 Ca (right, boxed) and stable intervals in spacing D and in adjacent intervals distributions D AIM with integers of the TF =161 kev. Z,N 14,18 16, ,18,21 A Z 32 Si 41 Ca E, D E + 1 (2 + ) D D AIM D D D D D AIM D E, D, D AIM E, D , 1944 n( TF ) n 12 1/ kev 322 kev 481 kev kev x=322 kev kev x=322 kev kev 1269 kev kev 1376 kev 1422 kev 1452 kev 1698 kev 1837 kev kev 0 00 Fig. 9 Spacing distribution in levels of in the regions 0-0 kev (top left) and 0-00 kev (bottom). Adjacent interval distributions for x=322 kev (top right, center) show maxima with the period TF =161 kev assigned to the tensor force action in odd Sb isotopes [6-9] (Table 2) kev

10 5 14 kev x=481 kev kev x=481 kev kev 481 kev x=14 kev 12 kev kev 1 kev 851 kev x=1941 kev 14 kev Fig. Spacing distribution in adjacent intervals in with maxima for x=481 kev (in both direction), x=12 kev and 1941 kev, rational relation between values of stable intervals 3:8:9:12=481:14:1452:1941 kev are presented in Table 2 (central columns).

11 kev 2 kev 8 kev 598 kev 664 kev 34 Cl kev 66 kev 1174 kev 1224 kev 1278 kev 11 kev kev 1758 kev 17 kev 1868 kev 18 kev 34 Cl 31 kev kev 34 Cl 1959 kev 34 Cl x=1758 kev 32 kev kev 66 kev 34 Cl x=1758 kev 3368 kev Fig. 11 Top: Spacing distribution in 34 Cl for energy region 0-00 kev. Bottom: Adjacent interval distribution for x=1758 kev with maxima at 32 kev and 66 kev (ratio 1:2).

12 Fig.12. Left: Distribution of E in all nuclei with A< (ENSDF, 1998). Right: Distribution of intervals adjacent to x=d=21 kev in 38 Ar spectrum []. Performed analysis [1,2] demonstrates the stability of energy intervals in nuclei situated at the border regions with the spin/orbit orientation of interacting nucleons (>,<). The stability is connected in these and heavier nuclei with the tensor force action which signals about the fundamental origin of nuclear intervals close or related to mass differences of the nucleon, pion and leptons. The remarkable proximity of parameters of the tuning effect in particle masses and nuclear mass/energies demonstrates the fundamental origin of the nucleon structure due to the QCD-based gluon quark-dressing effect. This effect should be studied with all nuclear data measured with high energy resolution. Harmonicity in the excitation of low-lying levels of nuclei situated in the border regions known in 33 S (left column of Table 3) extends as the grouping of E (shown in Fig.12 left) at 3936 kev close to six times the parameter 492 kev considered in these works. Table 3 Grouping effect at excitation of light nuclei around the value 3936 kev=6 492 kev. E, J π Shell isotope 33 S 33 Cl model 38 Cl 39 K 39 Ca 37 Ar 38 Ar E, 3/ E, 5/ interval diff., kev Authors appreciate the help by M.S.Sukhoruchkina in producing figures in these works. REFERENCES 1. S.I. Sukhoruchkin et al. Proc. ISINN-21, Dubna, JINR E , p.5 2. S.I. Sukhoruchkin et al., Proc. ISINN-22, Dubna, 14 (1,2,3-rd parts of work). 3. T. Otsuka, Phys. Scr. T 2 (13) 07. and references therein. 4. S.I. Sukhoruchkin, Nucl. Phys. B (Proc. Suppl.) 234C (13) S.I. Sukhoruchkin, Proc. Int. Conf. QCD14, Montpellier, 14 (in press). 6. Landolt-Boernstein New Series, vols. I/A,B. Springer, 12; vols. I/C,D,E, S.I. Sukhoruchkin et al. Proc. ISINN-19, JINR E3-12-, p S.I. Sukhoruchkin, Proc. ISINN-13, JINR, E3-06-7, p S.I. Sukhoruchkin, Z.N.Soroko, Proc. ISINN-, JINR E , p. 4.. S.I. Sukhoruchkin et al. Proc. ISINN-7, Dubna, JINR E , p. 313