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Clus e o a ional bands in 11B
Danilo , A.N.; Demyano a, A.S.; Ogloblin, A.A.; Belyae a, T.L.; Goncha o , S.A.;
T zaska, Wladyslaw
Danilo , A.N., Demyano a, A.S., Ogloblin, A.A., Belyae a, T.L., Goncha o , S.A., &
T zaska, W. (2016). Clus e o a ional bands in 11B. In V. G eco, M. L. Cogna a, S.
Pi one, F. Rizzo, & C. Spi ale i (Eds.), NN2015 : 12 h In e na ional Con e ence on
Nucleus-Nucleus Collisions 2015 (A icle 04011). EDP Sciences. EPJ Web o
Con e ences, 117. h ps://doi.o g/10.1051/epjcon /201611704011
2016
Clus e o a ional bands in 11B
A.N. Danilo 1, A.S. Demyano a1,A.A.Ogloblin
1,
T.L. Belyae a2,S.A.Goncha o
3and W. T zaska4
1Na ional Resea ch Cen e “Ku cha o Ins i u e” Moscow, 123182, Russia
2Uni e sidad Au onoma del Es ado de Mexico, Toluca, 50000, Mexico
3Lomonoso Moscow S a e Uni e si y, Moscow, 119991, Russia
4JYFL, Jy ¨askyl¨a, FIN-40500, Finland
Abs ac
Diffe en ial c oss-sec ions o 11B+αinelas ic sca e ing a E(α)=
65 MeV leading o mos o he known 11B s a es a exci a ion ene gies
up o 14 MeV we e measu ed [1]. The da a analysis was done using
Modified diff ac ion model (MDM) [2] allowing de e mining adii o
exci ed s a es. Radii o he s a es wi h exci a ion ene gies less han ∼
7 MeV coincide wi h he adius o he g ound s a e wi h an accu acy
no less han 0.1 - 0.15 m. This esul is consis en wi h adi ional
iew on shell s uc u e o low-lying s a es in 11B. Mos o he obse ed
high-ene gy exci ed s a es a e dis ibu ed among ou o a ional bands.
Momen s o ine ia o band s a es a e close o he momen o ine ia o
he Hoyle s a e o 12C. The calcula ed adii, ela ed o hese bands, a e
0.7 - 1.0 m la ge han he adius o he g ound s a e, and a e close
o he Hoyle s a e adius. These esul s a e in ag eemen wi h exis ing
p edic ions abou a ious clus e s uc u e o 11B a high exci a ion
ene gies.
1 In oduc ion
Du ing long ime 11B nucleus was conside ed as a good example o shell
effec s in ligh nuclei. Up o exci a ion ene gies ∼7MeV11B s a es we e
desc ibed by diffe en a ian s o shell models. Recen ly, howe e , a numbe
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
© The Au ho s, published by EDP Sciences SI . This is an open access a icle dis ibu ed unde he e ms
o he C ea i e
Commons A ibu ion License 4.0 (h p://c ea i ecommons.o g/licenses/by/4.0/).
F
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o heo e ical and expe imen al wo ks appea ed [3–5] wi h p edic ions abou
clus e configu a ions o a ious ypes co-exis ed in 11B.
Pa icula a en ion was d awn o he idea ha he e may be s a es
in 11B, which a e analogs o he amous 0+
2s a e in 12C nucleus ( he so-
called Hoyle s a e). The Hoyle s a e consis s o h ee weakly in e ac ing
alpha - clus e s and i s p ope ies we e c ucial o e ifica ion o he alpha -
pa icle condensa ion heo y [6]. One o he main sugges ions o his heo y
is abno mally la ge adius o he Hoyle s a e. Acco dingly, Hoyle s a e
analogs in 11B mus also ha e inc eased size.
I was assumed [3] ha he Hoyle s a e analog in 11B is he s a e 3/2−
wi h exci a ion ene gy 8.56 MeV, which is no desc ibed by any a ian o he
shell model. The adius o 8.56 MeV s a e was conside ed o be abno mally
la ge, and i was p edic ed ha his s a e is a base o o a ional band.
The e a e a lo o expe imen al s udies o 11B (see, e.g., [7] and e e ences
he ein), bu hey did no affec he exci a ion ene gy egion o in e es o
he p oblem. Due o he ac ha many ques ions abou 11B s a es emained
open, we ha e unde aken a new s udy o inelas ic 11B+αsca e ing a
E(α) = 65 MeV [1]. Expe imen al esul s we e analyzed using Modified
diff ac ion model (MDM). In his a icle we discuss esul s o high-ene gy
exci ed s a es and possible clus e o a ional bands o med om hem.
2 Radii and momen s o ine ia o high-lying
o a ional bands in 11B
The ollowing o a ional bands we e p edic ed [3,5] in high exci a ion ene gy
egion in 11B. Mos o hese s a es we e obse ed in ou expe imen :
K= 3/2−: 8.56 (3/2−) - 10.34 (5/2−) - 11.60 - 13.14 (9/2−)MeV,
K= 1/2+: 6.79 (1/2+) - 9.88 (3/2+) 11.60 (5/2+) 13.16 (7/2+)MeV,
K= 3/2+: 7.98 (3/2+) - 9.27 (5/2+) - 10.60 (7/2+) - 12.63 (9/2+)MeV,
K= 5/2+: 7.29 (5/2+) - 9.19 (7/2+) - 11.27 (9/2+)MeV.
These o a ional bands a e shown in Fig. 1 oge he wi h he band in
12C, based on he Hoyle s a e. Da a on angula momen um ans e wi h
exci a ion s a es belonging o he specified bands, ecei ed om ou expe -
imen , a e in ag eemen wi h known spin-pa i ies o 11B s a es. Howe e ,
o 6.79, 9.88, 10.34, 13.14 13.16 MeV s a es i could no de e mined un-
ambiguously due o insufficien ene gy esolu ion. Se e al special ea u es
in J(J+ 1) dependence o exci a ion ene gies can be seen in Fig. 1. Fi s ly,
momen s o ine ia o he band s a es a e e y high and compa able. The
la ges o hem (2I/¯h2∼4.0, by he ene gy diffe ence be ween he exci a ion
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Figu e 1: P edic ed [3,5] o a ional bands in 11B a exci a ion ene gies E∗>7MeV.
Fo compa ison, o a ional band [8], based on he Hoyle s a e (0+
2,7.65MeV)o
12C, is shown.
ene gies 11.60 and 10.34 MeV) a e obse ed o highe membe s o he o a-
ional band K= 3/2−, o which clus e s uc u e 2α+ is p edic ed. I is
in e es ing ha i is much la ge han he momen o ine ia o i s analog -
he Hoyle s a e, o which 2I/¯h2= 2.7. Secondly, he e is a clea co ela ion
be ween he momen s o ine ia and he alues o adii ob ained om sca -
e ing da a using MDM. Low-lying s a es o 11B ha e ”no mal” adii and
” educed” momen s o ine ia abou 2I/¯h2∼1.1. These alues a e close o
alues o he fi s exci ed s a e o 12C, 4.44 MeV. ”Big” momen s o ine ia
co espond o inc eased adii. Summa y o he adii o he s a es measu ed
using MDM is gi en in he Fig. 2.
As seen om Fig. 2, inc eased adii we e ound, a leas , o one o he
membe s o each band, and in mos cases hey a e abou 0.7 - 1.0 m la ge
han he adius o he g ound s a e o 11B. This leads o he conclusion ha
all s a es belonging o he bands unde conside a ion, ha e abno mal size.
Theo e ical wo ks [3–5] sugges a significan de o ma ion o he o a ional
s a es o 11Bwi hE∗>7 MeV and i allows he inc ease o hei adii. The
adii and momen s o ine ia o hese s a es a e close o he co esponding
alues o he Hoyle s a e in 12C nucleus and he o a ional band based on i .
These ac s indica e p obable clus e na u e o he 11B s a es discussed. In
pa icula , he 8.56 MeV s a e can be conside ed as an analog o he Hoyle
s a e. Bu some open ques ions emain ega ding he o a ional band ha
is based on he 6.79 MeV s a e, including he e y exis ence o band [1].
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Figu e 2: Dependence o R ms ( oo -mean-squa e adii, de e mined by MDM) on
he exci a ion ene gy o s a es o 11B. The sizes o he plo ed poin s a e p opo -
ional o he momen s o ine ia o he s a es.
Acknowledgemen s
The wo k was suppo ed in pa by g an s o Russian Science Founda ion
14-12-00079, Russian Founda ion o Basic Resea ches 14-02-00560 and 15-
02-01503 and he mobili y g an om he Academy o Finland
Re e ences
[1] A.N. Danilo , A.S. Demyano a e al., Physics o A omic Nuclei 78, No.
6, 777 (2015)
[2] A.N. Danilo e al., Phys.Re . C 80, 054603 (2009)
[3] Y. Kanada-Enyo, Phys. Re . C 75, 024302 (2007)
[4] T. Yamada and Y. Funaki, Phys. Re . C 82, 064315 (2010)
[5] H. Yamaguchi e al., Phys. Re . C83, 034306 (2011)
[6] 6. A. Tohsaki, H. Ho iuchi, P. Schuck, and G. Ropke, Phys. Re . Le .
87, 192501 (2001)
[7] N. Bu ebae e al., Physics o A omic Nuclei68, 1303 (2005)
[8] A.A. Ogloblin e al., EPJ Web o Con e ences, 66, 02074, (2014)
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