Pis’ma v ZhETF, vol. 114, iss. 6, pp. 351 - 352

Search for exotic states in¹³C

A. S. Demyanova⁺¹⁾, A. N. Danilov⁺, S. V. Dmitriev⁺, A. A. Ogloblin⁺, V. I. Starastsin⁺, S. A. Goncharov^∗,

D. M. Janseitov^×◦∇

⁺National Research Centre Kurchatov Institute, 123182 Moscow, Russia

^∗Lomonosov Moscow State University, 119991 Moscow, Russia

^×Joint Institute for Nuclear Research, 141700 Dubna, Russia

^◦Institute of Nuclear Physics, National Nuclear Center of Republic of Kazakhstan, 050032 Almaty, Republic of Kazakhstan

^∇Al-Farabi Kazakh National University, 050040 Almaty, Republic of Kazakhstan

Submitted 2 August 2021

Resubmitted 2 August 2021

Accepted 16

August 2021

DOI: 10.31857/S1234567821180014

¹³C is usually recognized a good example of a “nor-

some reservation because the used data were obtained

mal” nucleus well described by the shell model. Its level

at 1-2 energies. Later our group made two experiments

scheme is reliably determined up to the excitation en-

on scattering of α-particles on¹³C at 65 and 90 MeV

ergies ∼ 10 MeV. However, some new ideas and results

[8, 11, 12]. Previous results for the increased radii of the

renewed interest in¹³C. The most ambitious among

3.09 and 8.86 MeV states were confirmed. Some amaz-

them is hypothesis [1] about possible existence of α-

ing result was obtained for the 9.90 MeV state - de-

particle Bose-Einstein condensation (αBEC). Some fea-

creased radius [11, 12]. So in¹³C coexistence of different

tures of the condensate structure were predicted [1] and

structures is seen: neutron halo (3.09 MeV), cluster state

observed [2, 3] in the second 0⁺, 7.65 MeV state of¹²C

(8.86 MeV, analog of the Hoyle state), compact cluster

(so called Hoyle state). It was also suggested [4, 5] that

state (9.90 MeV) [11, 12]. Moreover, our team has suc-

the structures analogous to the Hoyle state may exist in

cessfully applied MDM to study of isobar-analog states

some neighbor nuclei, e.g.,¹³C. In [6] existence of two

(IAS) [13, 14]. Study of isobar-analog states in¹³N can

rotational bands built on the 3/2^-2, 9.90 MeV state and

be additional check of obtained results for¹³C states.

some yet not seen 3/2⁺ state was proposed. The radii of

First aim of this work was search for possible analogs

the members of the first band were predicted [7] to be

of the Hoyle state in excited states of¹³C. As mentioned

enhanced (more than 3 fm). Our results for the 9.90 MeV

in [5], possible candidate can be the 1/2^-3, 11.08 МeV

state [8] showed that the predicted radius enhancement

state. Previously increased radius for this state was de-

doesn’t take place. Recently a hypothesis was put for-

termined using MDM in [10] but this result was obtained

ward about a new type of symmetry in the¹³C - D^′3h

only based on data at single energy 388 MeV [4]. This is

symmetry [9]. On the basis of D^′3h symmetry, the rota-

upper energy limit for MDM application. So new exper-

tional nature of a whole group of low-lying¹³C states

imental data were very desirable. The 11.08 MeV state

was predicted. If this hypothesis is confirmed, our under-

was observed in both experiments at 65 and 90 MeV

standing about the¹³C structure will radically change.

[8, 11, 12]. We applied MDM to this new experimental

Thus, a critical analysis of the available data is required

data. Averaged on two energies rms radius is 2.8±0.2 fm.

to answer the question about the nature of low-lying

This value within errors coincides with the radius of the

excited¹³C states.

8.86 MeV state in¹³С and the Hoyle state in¹²С and is

Recently another approach was proposed for mea-

smaller than predictions [5]. It can be an argument to

suring the radii of nuclei in the excited states, the mod-

possible close structure of these states.

ified diffraction model (MDM) [3]. Its application [10]

to the analysis of existing quite scarce literature data

Second aim is question about the 9.90 MeV state.

demonstrated that the radii of some states in¹³C really

Our previous MDM analysis has shown that the 9.90

are enhanced. However, this result should be taken with

MeV state 3/2^- is compact [11, 12]. While some theo-

retical works [7] contradict this result and predict radius

¹⁾e-mail:a.s.demyanova@bk.ru

enhancement for the 9.90 MeV state. Moreover, it was

Письма в ЖЭТФ том 114 вып. 5 - 6

2021

351

352

A. S. Demyanova, A. N. Danilov, S. V. Dmitriev et al.

proposed in [9] that the 9.90 MeV state is member of ro-

tational band K^π = 1/2^- based on the 8.86 MeV state.

1. A. Tohsaki, H. Horiuchi, P. Schuck, and G. Röpke, Phys.

As the 8.86 MeV state has increased radius, quite nat-

Rev. Lett. 87, 192501 (2001).

ural that other members of the band should also have

2. M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-

increased radius.

Cosel, and A. Richter, Phys. Rev. Lett. 98, 032501

To check these results we study the isobar-analog

(2007).

state of the 9.90 MeV state in¹³N - the 9.48 MeV state

3. A. N. Danilov, T. L. Belyaeva, A. S. Demyanova,

using MDM [14]. Several works have been found in the

S. A. Goncharov, and A. A. Ogloblin, Phys. Rev. C 80,

literature on the reaction¹³C(³He, t)¹³N at 43.6 MeV

054603 (2009).

[15] and 450 MeV [16] with the excitation of the 9.48

4. T. Kawabata, Y. Sasamoto, M. Fujiwara et al.

MeV state. We applied MDM to these data. There are

(Collaboration), Journal of Physics: Conference Series

two variants of determining radius [14] using MDM

111, 012013 (2008).

based on charge-exchange reactions. We obtained fol-

5. T. Yamada and Y. Funaki, Int. J. Mod. Phys. E 17,

lowing results for the 9.48 MeV state: 2.5 ± 0.3 fm for

2101 (2008).

the first variant and 2.3 ± 0.3 fm for the second. So,

both variants gave practically the same result: we ob-

6. M. Milin and W. von Oertzen, Eur. Phys. J. A 14, 295

(2002).

tained normal, non-increased radius for the 9.48 MeV

state, which within errors coincides with the radius of

7. N. Furutachi, M. Kimura, Phys. Rev. C 83, 021303

(2011).

the ground state. But the data at 450 MeV is on the

upper limit of the MDM applicability and, therefore,

8. A. A. Ogloblin, A. S. Demyanova, A. N. Danilov,

additional verification is required. So a new experiment

S. A. Goncharov, T. L. Belyaeva, W. Trzaska, and

Yu. G. Sobolev, JETP Lett. 102, 199 (2015).

with³He beam at middle energies is highly desireable.

Also we have clarified radius of the 9.90 MeV state

9. R. Bijker and F. Iachello, Phys. Rev. Lett. 122, 162501

based on existing experimental data. Averaged on 65

(2019).

and 90 MeV rms radius is 2.0 ± 0.3 fm. Obtained value

10. A. S. Demyanova, A. A. Ogloblin, A. N. Danilov,

of the radius practically coincided with value from [8]

T. L. Belyaeva, and S. A. Goncharov, Int. J. Mod. Phys.

E 20, 915 (2011).

but value of error is a bit larger. In principle, within

the error limits, the value of the radius obtained for

11. A. S. Demyanova, A. N. Danilov, S. V. Dmitriev et al.

the 9.90 MeV in¹³C coincides with the radius of the

(Collaboration), EPJ Web of Conferences 66, 02027

(2014).

9.48 MeV state in¹³N state and radius of the g.s in¹³C;

perhaps, due to rather large value of errors, values are

12. A. S. Demyanova, A. A. Ogloblin, A. N. Danilov,

similar.

S. A. Goncharov, T. L. Belyaeva, Yu.G. Sobolev,

S. V. Khlebnikov, N. Burtebaev, W. Trzaska, P. Heikki-

It is interesting to note that the 9.90 MeV state

nen, G. P. Tyurin, D. Janseitov, and Yu. B. Gurov, EPJ

is strongly excited in the α-cluster transfer reactions

Web of Conferences 117, 04012 (2016).

(⁶Li,d) and (⁷Li,t) on⁹Be [17] while the 8.86 MeV state

13. A. S. Demyanova, A. A. Ogloblin, A. N. Danilov,

is not. This means that α-cluster structures of the 8.86

T. L. Belyaeva, S. A. Goncharov, and W. Trzaska, JETP

and 9.90 MeV states are probably different: the latter

Lett. 104(8), 526 (2016).

has a strong⁹Be + α component which is absent in the

14. A. S. Demyanova, A. A. Ogloblin, S. A. Goncharov,

8.86 MeV. So, 8.86 and 9.90 MeV states can’t be mem-

A. N. Danilov, T. L. Belyaeva, and W. Trzaska, Physics

bers of one band due to different structures and rms

of Atomic Nuclei 80, 831 (2017).

radii and proposed in [9] band K^π = 1/2^- most likely

15. R. J. Peterson, J. R. Shepard, and R. A. Emigh, Phys.

doesn’t exist. At the same time, proposed in [6] band

Rev. C 24, 826 (1981).

K^π = 3/2^- can exist and members of this band should

16. H. Fujimura, H. Akimune, I. Daito, M. Fujiwara,

have normal rms radius. Anyhow, question regarding ro-

K. Hara, K. Y. Hara, M. N. Harakeh, F. Ihara, T. Ino-

tational states and bands in¹³C is still open and deeper

mata, K. Ishibashi, T. Ishikawa, T. Kawabata, A. Tamii,

analysis is needed.

M. Tanaka, H. Toyokawa, T. Yamanaka, and M. Yosoi,

The reported study was funded by Russian Founda-

Phys. Rev. C 69, 064327 (2004).

tion for Basic Research, project number 20-32-70115.

17. V. Z. Goldberg, V. V. Davidov, A. A. Ogloblin,

This is an excerpt of the article “Search for exotic

S. B. Sakuta, and V. I. Tshuev, Proc. of Soviet Academy

states in¹³C”. Full text of the paper is published in

of Science, Ser. Fiz. 35, 1663 (1971).

JETP Letters journal.

DOI: 10.1134/S0021364021180016

Письма в ЖЭТФ том 114 вып. 5 - 6

2021