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Molecular bands in 22Ne
ELSEVIER
Nuclear Physics A738 (2004)447450 www.elsevier.comilocate/npe
Molecular bands in "Ne hI. Dufour
a
and P. Descouvemont
*
IReS Bat27, Ii\JZP:~~CNRS/Cniversiti, Louis Past,eur BP28, F-67037 Strasbourg Cetlex 2; France
a
"Physique Nuc1Pair.r Thborique et Physique Mathi.niatique, CP229, Universiti. Libre dc Urnxelles, B1050 Brussels, Brlgium
0-cluster states o f "’Ye are investigated with a ( Y + ’ ~ Otwo-cluster model, using the Generator Coordinate Method. The l80internal wave functions are defined in t,he shell niotlel involving t h c s , p and sd shells. a consequence, the model allows thc description of many a+180 chanriels. In this paper, wc forus only on two results, particularly significant in the corit,cxt of this work : the possiblc mist,ence of a positive-parit,y molecular band and the confirriiation of the existence of ncyyt,ive-parity doublets locatcd above the a+l8O threshold.
1. Introduction
Microscopic clust,er models appear to be well-atlapted to t,he description of i u m y nuclear systems part,iciilarly those presenting states with a marked a structure. In this context, me have developed a ncw a+180 two-cluster model using the Generator Coordinate Method (GCILl) which aims 1,o improve the "0 internal wiwe functions. Indeed, they arc defined in the shell model irivolving the filled s, p shells phis two neutrons in t,hr s d shell [l]. As a consequcncr, t h : model allows the descriptiori of many a+lSO channels. ?’his point is very interesting i n the context of 22Ne wherc~many experimental states are knownl typically around 50 states below the a+I8O thrwhold. In this way; the Extcritled TwoCluster Model (ETChI) developed here represents a significant improvement, as compared to preiious simplcr approaches [2,3].Nore details are given in ref. [l].In this paper; we focus 011 two results where the predictive power of tlip ETCiLl becomes particulary visible : the possible existtwx of a posit,ive-parity molecular band and the confirrriiition of the existence of negatjivr-parity doublets located abovc: the a+I80 threshold r c p o r t d in the experiment of Rogadiev et al. [4].
’Directcur de Rechercht.~FNRS see front matter 0 2004 Elsevier B.V All rights reserved doi:10.1016!j.nuclphysa.2004.04.083
0375-9474K
~
M.Dufoul; R DescouveinontiNuclcar Physics -4 738 (2004) 447-450
448
2. The Extended Two-Cluster Model
In a microscopic model: thcl a+"O systcrri is treated as a system of d = 22 interacting nucleons. The corresponding Hamiltoniari is defined as
\,;?-’
where is the lhlkov interaction. I$" is a Spin-Orbit interaction and 1;: is the Coulomb interaction. In the ETCM,the 22Ne~vavefunctions can be scheInatically written as
where $ Q is~ the ~ ~internal wave function of the "0 in t,hc chaiinel labelleti by c, ( j n is the internid function of t,he a particle obtained in a straightforward way from the wave function of a s cluster and g r ( p ) is the relative wave funckiori depending on thr relative coordinat,c p. A is the A-nucleon antisymnrct,rizer. In the shell-model framework considered h u e , we get fourteen different "O( 1: ) states labelled ~ J J Tthe spin I1 of "0 : three with 1: =:’0 two with 1: =;’1 five with 1 : = 2+, t>vo with 1; = 3- and two with 1 : = .’4 In this nay, m m y channels of t,he 0 + ’ ~ 0 system citn be iricluded in the extended GCM basis which appears particularly powerful to descrih: a large number of 22Ne states [l]. 3. A new molecular band
Our results suggest the cxisterice of a so-cirllrd iiiolecular band located above. the a+180 threshold. The energies ;tnd reduced (Y witlt,h are given in Table 1. The E2 rediiced transitioii probabilities are given in Table 2 with the correspoiiding Fa,.
Table 1 Energies (in hley-). reduced
cy
n-idths (in %) and
J"
E:p
@’(a = 11.6 fm)
o+
2.1
21 4+
2.6 4.2
8.3 5.9 7.0
ra (in keV) of the molecular states B2(a= 5 fm) rn 93 93 100
60 53 140
We can riotice that this set of states prwent similar large reduced a widths in the entrance c:hanriel [here at ’xO(O:)] and similar and largc B ( E 2 ) valiies h t wctn t,hem. These properties are clear signatures of stiitrs presenting a largc clust eriiig a s expected for molec~iilarstates. i\w cxperimental irivt3stigations moiiltl be ~velconic i n order to confirm the existence of’ t,liis l ~ a n d .
M. Dujow F Descouuemont/Nuclenr Physics A738 (2004) 447-450
449
’Table 2 E2 reduccd transition probwbilitics (in W.U.) between the rnoleciilar band
4. Splitting of tv-cluster states
This sectlion is ticvoted to the splitting of a-clust,er st,ates reported in the experiment of Rogachev et ad. [4]. The physical propertios of these states are summarized in Table 3.
Table 3 Energies (in MeV)>reduced a widths (in 9%) and (in keV) of J" EF" E:%. B&(a = 5 fm) 6’&ni(a = 5 fm) 1, 12.58 2.91 2.91 10 13 8 1; 12.84 3.17 3.86 20 13 3.52 3.25 19 3; 13.19 3.74 4.02 11 11 3; 13.41 4.01 23 3 5100 5.02 8 52 7- (19.28) (9.61) 9.12 5 7- (19.56) (9.89) 9.89 81 11.18 51 9- 20.85 9- 21.84 12.17 57
ra
the doublets in
22Ne
ra 42 115 11 40 7 111 235 428
Our calculations confirm the existence of the 1- arid 3- doublets. They predict candidates for. the 5- arid 7- doublets. The experimental 7- states are not definitely assigned and their energies are given in parentheses in Table 3. We predict a 7- doublct in this energy rc,gion. The experimental 9- doublct is not confirmed by our calculatiori. B(E1) and B ( E 2 ) values, with the associated rr, are given in Table 4. .4n important remark associated with thcse stat,es is that t,heir striict,ures are signific:ant,ly mixed. This means that t,ht:se peculiar states, in spite of t,heir dominant, reduced width in the Q + " O ( O ~ ) cliannel, must be considered as a mixing of several C L + ’ ~ Ocoil* figurations. We gct similar doublets in the a+18N stem. The physical properties are published in ref. [I]. 5 . Conclusion The iniprovement of the I8O internal wavt functions considcred here allows the description of "Ne cluskr states, that previous simpler approaches were unal)le to account for. In particular, we hiwe been able to study the splitting of negative-parity a-cluster states reported in the experiment of Rogachev et al. [4]. 0111. calculation iridicat,es that thestr
450
M. DufouI; El DescouLeinorzt/Nuclear Ph,vsics A738 (2004) 447-450
Table -I RI and E2 reduced transition protjabilities (iri W.U.) between states of the doublets arid states of the 0: barid.
3, 3; 3,
1,
2.9
1, 1,
14.7
9 : 4 B(E1) 3.4 x lo-" 6.4 x lo-’’ 6.7 x 1 0 P 3.6 x lo-" 9.4x 10-4 5.8x l o p 4
3.9x 10 * 7.2 x 10-5 2.3x 10
r,(ev) 0.36
0.84 5.8 4.0 0.89 0.67
st,atcs must be interpreted as a strong mixing of CU+’~O* configurations. Our calculation also suggcsts the existence of a positive-parity molecular band locat,ed above the a+180 tliresholtl. New experimental investigations mould therefore be particularly interesting in order t,o confirm thc existence of this cluster states in the. a+"0 system arid also iri the tr+"Ke system.
REFERENCES 1. 11. Dufour and P. Descouvmiont, Nucl. Phys. A4726(2003) 53. 2. I(.Limgankc, D. Frekers arid R. Staclemarin, A. IYeiguny: Nucl. Phys.
40. 3. f.Dr:scouvernorit, Phys. Rcv. C 38 (1988)2397. 4. C:. 17. Rogat:hev et d ,Phy-s. Rev. C 64 (2001) 031302.
iZ 402 (1983)
Nuclear Physics A738 (2004)447450 www.elsevier.comilocate/npe
Molecular bands in "Ne hI. Dufour
a
and P. Descouvemont
*
IReS Bat27, Ii\JZP:~~CNRS/Cniversiti, Louis Past,eur BP28, F-67037 Strasbourg Cetlex 2; France
a
"Physique Nuc1Pair.r Thborique et Physique Mathi.niatique, CP229, Universiti. Libre dc Urnxelles, B1050 Brussels, Brlgium
0-cluster states o f "’Ye are investigated with a ( Y + ’ ~ Otwo-cluster model, using the Generator Coordinate Method. The l80internal wave functions are defined in t,he shell niotlel involving t h c s , p and sd shells. a consequence, the model allows thc description of many a+180 chanriels. In this paper, wc forus only on two results, particularly significant in the corit,cxt of this work : the possiblc mist,ence of a positive-parit,y molecular band and the confirriiation of the existence of ncyyt,ive-parity doublets locatcd above the a+l8O threshold.
1. Introduction
Microscopic clust,er models appear to be well-atlapted to t,he description of i u m y nuclear systems part,iciilarly those presenting states with a marked a structure. In this context, me have developed a ncw a+180 two-cluster model using the Generator Coordinate Method (GCILl) which aims 1,o improve the "0 internal wiwe functions. Indeed, they arc defined in the shell model irivolving the filled s, p shells phis two neutrons in t,hr s d shell [l]. As a consequcncr, t h : model allows the descriptiori of many a+lSO channels. ?’his point is very interesting i n the context of 22Ne wherc~many experimental states are knownl typically around 50 states below the a+I8O thrwhold. In this way; the Extcritled TwoCluster Model (ETChI) developed here represents a significant improvement, as compared to preiious simplcr approaches [2,3].Nore details are given in ref. [l].In this paper; we focus 011 two results where the predictive power of tlip ETCiLl becomes particulary visible : the possible existtwx of a posit,ive-parity molecular band and the confirrriiition of the existence of negatjivr-parity doublets located abovc: the a+I80 threshold r c p o r t d in the experiment of Rogadiev et al. [4].
’Directcur de Rechercht.~FNRS see front matter 0 2004 Elsevier B.V All rights reserved doi:10.1016!j.nuclphysa.2004.04.083
0375-9474K
~
M.Dufoul; R DescouveinontiNuclcar Physics -4 738 (2004) 447-450
448
2. The Extended Two-Cluster Model
In a microscopic model: thcl a+"O systcrri is treated as a system of d = 22 interacting nucleons. The corresponding Hamiltoniari is defined as
\,;?-’
where is the lhlkov interaction. I$" is a Spin-Orbit interaction and 1;: is the Coulomb interaction. In the ETCM,the 22Ne~vavefunctions can be scheInatically written as
where $ Q is~ the ~ ~internal wave function of the "0 in t,hc chaiinel labelleti by c, ( j n is the internid function of t,he a particle obtained in a straightforward way from the wave function of a s cluster and g r ( p ) is the relative wave funckiori depending on thr relative coordinat,c p. A is the A-nucleon antisymnrct,rizer. In the shell-model framework considered h u e , we get fourteen different "O( 1: ) states labelled ~ J J Tthe spin I1 of "0 : three with 1: =:’0 two with 1: =;’1 five with 1 : = 2+, t>vo with 1; = 3- and two with 1 : = .’4 In this nay, m m y channels of t,he 0 + ’ ~ 0 system citn be iricluded in the extended GCM basis which appears particularly powerful to descrih: a large number of 22Ne states [l]. 3. A new molecular band
Our results suggest the cxisterice of a so-cirllrd iiiolecular band located above. the a+180 threshold. The energies ;tnd reduced (Y witlt,h are given in Table 1. The E2 rediiced transitioii probabilities are given in Table 2 with the correspoiiding Fa,.
Table 1 Energies (in hley-). reduced
cy
n-idths (in %) and
J"
E:p
@’(a = 11.6 fm)
o+
2.1
21 4+
2.6 4.2
8.3 5.9 7.0
ra (in keV) of the molecular states B2(a= 5 fm) rn 93 93 100
60 53 140
We can riotice that this set of states prwent similar large reduced a widths in the entrance c:hanriel [here at ’xO(O:)] and similar and largc B ( E 2 ) valiies h t wctn t,hem. These properties are clear signatures of stiitrs presenting a largc clust eriiig a s expected for molec~iilarstates. i\w cxperimental irivt3stigations moiiltl be ~velconic i n order to confirm the existence of’ t,liis l ~ a n d .
M. Dujow F Descouuemont/Nuclenr Physics A738 (2004) 447-450
449
’Table 2 E2 reduccd transition probwbilitics (in W.U.) between the rnoleciilar band
4. Splitting of tv-cluster states
This sectlion is ticvoted to the splitting of a-clust,er st,ates reported in the experiment of Rogachev et ad. [4]. The physical propertios of these states are summarized in Table 3.
Table 3 Energies (in MeV)>reduced a widths (in 9%) and (in keV) of J" EF" E:%. B&(a = 5 fm) 6’&ni(a = 5 fm) 1, 12.58 2.91 2.91 10 13 8 1; 12.84 3.17 3.86 20 13 3.52 3.25 19 3; 13.19 3.74 4.02 11 11 3; 13.41 4.01 23 3 5100 5.02 8 52 7- (19.28) (9.61) 9.12 5 7- (19.56) (9.89) 9.89 81 11.18 51 9- 20.85 9- 21.84 12.17 57
ra
the doublets in
22Ne
ra 42 115 11 40 7 111 235 428
Our calculations confirm the existence of the 1- arid 3- doublets. They predict candidates for. the 5- arid 7- doublets. The experimental 7- states are not definitely assigned and their energies are given in parentheses in Table 3. We predict a 7- doublct in this energy rc,gion. The experimental 9- doublct is not confirmed by our calculatiori. B(E1) and B ( E 2 ) values, with the associated rr, are given in Table 4. .4n important remark associated with thcse stat,es is that t,heir striict,ures are signific:ant,ly mixed. This means that t,ht:se peculiar states, in spite of t,heir dominant, reduced width in the Q + " O ( O ~ ) cliannel, must be considered as a mixing of several C L + ’ ~ Ocoil* figurations. We gct similar doublets in the a+18N stem. The physical properties are published in ref. [I]. 5 . Conclusion The iniprovement of the I8O internal wavt functions considcred here allows the description of "Ne cluskr states, that previous simpler approaches were unal)le to account for. In particular, we hiwe been able to study the splitting of negative-parity a-cluster states reported in the experiment of Rogachev et al. [4]. 0111. calculation iridicat,es that thestr
450
M. DufouI; El DescouLeinorzt/Nuclear Ph,vsics A738 (2004) 447-450
Table -I RI and E2 reduced transition protjabilities (iri W.U.) between states of the doublets arid states of the 0: barid.
3, 3; 3,
1,
2.9
1, 1,
14.7
9 : 4 B(E1) 3.4 x lo-" 6.4 x lo-’’ 6.7 x 1 0 P 3.6 x lo-" 9.4x 10-4 5.8x l o p 4
3.9x 10 * 7.2 x 10-5 2.3x 10
r,(ev) 0.36
0.84 5.8 4.0 0.89 0.67
st,atcs must be interpreted as a strong mixing of CU+’~O* configurations. Our calculation also suggcsts the existence of a positive-parity molecular band locat,ed above the a+180 tliresholtl. New experimental investigations mould therefore be particularly interesting in order t,o confirm thc existence of this cluster states in the. a+"0 system arid also iri the tr+"Ke system.
REFERENCES 1. 11. Dufour and P. Descouvmiont, Nucl. Phys. A4726(2003) 53. 2. I(.Limgankc, D. Frekers arid R. Staclemarin, A. IYeiguny: Nucl. Phys.
40. 3. f.Dr:scouvernorit, Phys. Rcv. C 38 (1988)2397. 4. C:. 17. Rogat:hev et d ,Phy-s. Rev. C 64 (2001) 031302.
iZ 402 (1983)