^7 Li elastic scattering and the lithium-induced reaction of one-nucleon transfers from ^10 B( ^7 Li, ^6 Li) ^11 B have been measured at E_LAB ( ^7 Li) = 58 MeV using U-400 accelerator beam of the FLNR JINR, Dubna. Angular distribution for reaction ^10 B( ^7 Li, ^6 Li) ^11 B with excitation of the 3.56 MeV state ( ^6Li^* ) is presented for the first time. The ‘‘Finite Range Distorted Wave Born Approximation’’ (FRDWBA) analysis of the differential cross section of the ^10 B( ^7 Li, ^6 Li) ^11 B ground state (g.s.) transition and excited ( J^π=0^+ , T=1 , E=3.56 MeV) state of ^6 Li transition was performed. Phenomenological approach based on solving an approximate equation for the reaction form factor was used to determine its radial dependence and empirical values of asymptotic normalization coefficient (ANC). The obtained values of ANC for the ^6 Li _g.s and ^6Li^* (3.56 MeV) states are in agreement with the literature ones. Comparison of the radial dependences of form factors shows that the wave function of the ^6 Li nucleus in excited ( J^π=0^+ , T=1 , E=3.56 MeV) state has increased spatial dimension compared to the ground state. This result is an argument in favor of a halo existence in ^6Li^* (3.56 MeV) state, while the question of a halo in ^6 Li _g.s. still stays open.

An intensive study of four-nucleon correlations of the α-cluster type initiated more than 50 years ago established their important role in nuclei. The microscopic α-cluster models have succeeded in describing the structure of many states in light nuclei, in particular, around the threshold energy of breakup into constituent clusters. Considerable attention has been drawn to the studies of α-cluster states in 12C, especially the second 0+ state, located at Ex=7.65 MeV, which is 0.38 MeV above the 3α threshold. This state was called the Hoyle state by the name of the astrophysicist who predicted it. Detailed analysis of the structure of 12C with the microscopic 3α cluster model was made about 30 years ago. The 3α generator coordinate method (GCM) and 3α resonating group method (RGM) calculations showed that the 7.65 MeV 0+2 state in 12C has a loosely coupled 3α structure and an enlarged radius. Modern microscopic calculations in the framework of cluster models such as the antisymmetrized molecular dynamics (AMD) and the fermionic molecular dynamics (FMD) also predict an increased radius of this above-threshold cluster state. A question naturally arises: do analogs of the Hoyle state exist in more massive 4N nuclei. First possible candidate is the 16O. Our analysis within Modified diffraction model has shown that 0+2 - 0+6 states which were named as possible analogs of the Hoyle state have normal non-increased radii. The next goal is 20Ne. The root mean square radii of 20Ne in the short-lived excited states were estimated for the first time from the analysis of α + 20Ne diffraction scattering. Differential cross sections of the elastic and inelastic α + 20Ne scattering in the incident energy range from a few MeV/nucleon up to 100 MeV/nucleon were analyzed by the modified diffraction model. No significant radius enhancement for the members of Kπ = 01+ and Kπ = 2− bands in comparison with the ground state was observed. At the same time 20% radius enhancement was obtained for the Kπ = 01− band members. Moreover, for the 02+ state located above α-emission threshold increased radius was observed. This result can speak in favor of possible α-condensate structure of the 02+ state and can be considered as a possible analog of the famous 7.65-MeV 02+ Hoyle state of 12C.

The review is concerned with studies of one-nucleon and two-nucleon halos in isobar analog states of light nuclei with A = 6, 12, 13, 14 . The study allow us to investigate manifestations of isotopic invariance in new objects and to relate properties of the neutrino and proton halos. The existence of a halo in isobar analog states has been little studied experimentally so far. It is proposed to solve the problem of experimentally determining the radii of some possible halo states in nuclei from 6Li to 14O that make up isobar analog doublets and triplets. New possible halo candidates are found in the 13C and 13N mirror nuclei, in the A = 12 and A = 14 isobar analog multiplets. Note that the isobar analog states with T = 1 in the A = 12 triplet are experimentally investigated for the first time in the transfer and charge-exchange reactions. It is established that the root-mean-square radii of the 0^ + states in the A = 6 multiplet coincide within errors. The results are obtained by two independent methods, ANC and MDM.

Проведен теоретический анализ имеющихся экспериментальных данных по упругому и неупругому рассеянию \(\alpha+^{13}\) С в области энергий до 90 МэВ. Получены параметры полумикроскопического потенциала в рамках дисперсионной оптической модели (SMDOM). Найденные потенциалы использованы при анализе в рамках метода искаженных волн недавно измеренных нами данных по неупругому рассеянию при энергиях 65 и 90 МэВ. Экспериментальные данные для состояний 3.68 и 7.55 МэВ представлены впервые. Состояния 3.68 и 7.55 МэВ рассмотрены в предположении принадлежности вращательной полосе основного состояния в рамках стандартной вращательной модели. Получено удовлетворительное описание угловых распределений, и определены значения длин деформации. Для остальных возбуждений до энергий 11 МэВ использован моделируемый феноменологический формфактор. Проведенный анализ подтвердил наличие нейтронного гало в состоянии 3.09 МэВ. Сходство формы полученных неупругих формфакторов для состояний 8.86, 10.996 и 11.08 МэВ, а также близость их радиусов дают основание полагать, что ядро \({}^{13}\) C во всех трех состояниях имеет увеличенные размеры и схожую структуру. Сравнение радиальных зависимостей формфакторов для состояний 9.90 и 8.86 МэВ показывает, что волновая функция состояния 9.90 МэВ имеет существенно меньшую пространственную протяженность. Полученные результаты согласуются с величинами радиусов обсуждаемых состояний, определенными в рамках Модифицированной дифракционной модели.

A theoretical analysis of available experimental data on elastic and inelastic α+^13 C scattering in the energy region extending up to 90 MeV is performed. The parameters of a semimicroscopic potential are found on the basis of the dispersive optical model. The potentials found in this way are used in analyzing, by the distorted-wave Born approximation, data that the authors recently measured for inelastic scattering at energies of 65 and 90 MeV. Experimental data for the states at 3.68 and 7.55 MeV are presented for the first time. These states are considered under the assumption that, within the standard rotational model, they are members of the ground-state rotational band. A satisfactory description of angular distributions is obtained, and deformation lengths are determined. A model phenomenological form factor is used for the remaining excitations in the energy range extending up to 11 MeV. The present analysis confirms the presence of a neutron halo in the 3.09-MeV state. A similarity of form of the inelastic form factors obtained for the 8.86-, 10.996-, and 11.08 MeV states and the proximity of their radii gives grounds to assume that the ^13 C nucleus in these three states has an enhanced size and similar structures. A comparison of the radial dependences of the form factors for the 9.90- and 8.86-MeV states shows that the wave function for the 9.90-MeV state has a substantially smaller spatial extension. These results agree with the values obtained for the radii of the states under discussion on the basis of the modified diffraction model.

An overview is provided for a new class of states, which we have named as the size isomers. Such states are weakly bound and have an exotic structure (cluster states, halo/‘‘skin’’). The development of methods for measuring the radii of nuclei in their short-lived excited states led to the discovery of new classes of states. The size of a nucleus defined by the radius of its nucleon (proton and neutron) density distribution and the proton charge distribution is one of the most fundamental and important nuclear characteristics. Nuclear radius determines the basic properties of nuclei and is a consequence of the fundamental features of the strong interaction. Up to now two groups of the size isomers were identified: the excited states with halos ( ^9 Be, ^11 Be, ^13 C, ^13 N) and some specific alpha-cluster states ( ^11 B, ^12 C, ^13 C). All the observed states are dilute, however, some indication to possible existence of more compact than the ground states was obtained as well (in ^13 C). The phenomenon of size isomerism occurred to be not a rare one especially if we take into account rotational bands based on some of such states. The structure of size isomers is related with some new features, e.g., rotating halos, halos in continuum, different types of quasimolecular configurations. Some rudimentary signs of alpha-particle condensation (a ‘‘ghost’’ of condensate) were observed in the Hoyle state of ^12 C, however, we cannot speak about confirmation of this ambitious theory. Analogs to the Hoyle state, expected in ^11 B, ^13 C, ^16 O, ^20 Ne near the α -emission thresholds, are considered.

The famous 7.65-MeV 0 ^+_2 Hoyle state of ^12 C is always attracting plenty attention. This state has dilute 3 α configuration and plays important role in nucleosynthesis. Question is if there are states analog to the Hoyle state in other 4 N nuclei. It is possible that α -cluster 0 ^+_2 state in ^20 Ne can be considered as an analog of the 7.65-MeV 0 ^+_2 Hoyle state of ^12 C.

The root mean square radii of $^{20}$Ne in the short-lived excited states were experimentally deduced for the first time from the analyses of $\alpha$+$^{20}$Ne diffraction scattering. Differential cross sections of the elastic and inelastic $\alpha$+$^{20}$Ne scattering in the incident energy range from a few MeV/nucleon up to 100 MeV/nucleon were analyzed by the modified diffraction model. No significant radius enhancement for the members of K$^{\pi}$ = 0$_{1}^{+}$ and K$^{\pi}$ = 2$^{-}$ bands in comparison with the ground state was observed. At the same time 20 % radius enhancement was obtained for the K$^{\pi}$ = 0$_{1}^{-}$ band members. Moreover, for the 0$_{2}^{+}$ state located above $\alpha$-emission threshold increased radius was observed. This result can speak in favor of possible $\alpha$-condensate structure of the 0$_{2}^{+}$ state and can be considered as a possible analog of the famous 7.65-MeV 0$_{2}^{+}$ Hoyle state of $^{12}$C.

The purpose of this research is to search and study halo in isobar-analog states of light nuclei. The study of states with a halo in isobar analogs allows one to investigate the manifestation of isotopic invariance at new objects and to relate the properties of the neutron and proton halo. The question of the existence of halo in isobar-analog states has so far not been practically raised in the experimental plan. The proposed approach is based on measuring the radii of states in which the halo exists or can exist. The data on the radii can give new information for solving the long-standing problem of a single description of the halo in both parts of the spectrum - discrete and continuous. We propose to solve problem: experimentally determine the radii of a number of states in which there can be a halo in nuclei, forming isobar-analog doublets and triplets. We have discovered new possible candidates for a halo in the isobar-analog multiplets A = 12 and A = 14. First, most of the states lie in the continuous spectrum. Second, the results were obtained within the framework of two independent methods: ANC and MDM. A great achievement was the development of the ANC method for studying resonance states, which made it possible to identify new cases of a proton halo in isobaric analog states.

We demonstrate that the radii of excited nuclear states can be estimated using the (3He, t) charge-exchange reaction and relying on the modified diffraction model.The radius of the 13 N excited state with an excitation energy of E*=2.37 MeV,which lies in a continuous spectrum, is determined. The radius of this state proves to be close to that of the mirror 3.09-MeV state of the 13 C nucleus, which possesses a neutron halo but lies in a discrete spectrum. Thereby, we demon- strate that the 2.37-MeV state of the 13 N nucleus has a proton halo. The analysis is based on published measurements of differential cross sections for relevant reactions.

C-13 is a good example of a "normal" nucleus that is well described within the shell model. Its level scheme is reliably determined up to excitation energies similar to 10 MeV. However, some questions remain open regarding the structure of low-lying C-13 states. This leads to the increased attention to C-13. In 2014, our group announced the discovery of a state of C-13 with an abnormally small radius. In the framework of the modified diffraction model (MDM) method, analyzing data on alpha-scattering on C-13 at 65 and 90 MeV, it was shown that this state has a radius reduced by 10%. At the same time, theoretical works predict dilute structure and increased radius for this state, and assumptions were made about its rotational structure. Another important question is the search for possible analogues of the Hoyle state in C-13. Confirmed analog of the Hoyle state is the 1/2(-)(8.86 MeV) state in C-13. Another possible candidate is the next 1/2(-) state - 11.08 MeV. Moreover, a hypothesis was put forward about a new type of symmetry in the C-13 structure - D-3h' symmetry. On the basis of D-3h' symmetry, the rotational nature of a whole group of low-lying C-13 states was predicted. In the work, 6 rotational bands were proposed, that is, almost all low-lying C-13 states were distributed among the rotational bands. Thus, a critical analysis of the available data is required to answer the question about the nature of low-lying excited states in C-13.

New experimental data on the inelastic scattering of α-particles on 13C at $$E(\alpha ) = 65$$ and 90 MeV with the excitation of the $$1{\text{/}}2_{3}^{ - }$$ state are reported. Data are analyzed using the modified diffraction model. The determined rms radius of this state coincides within errors with the radius of the $$1{\text{/}}2_{2}^{ - }$$ 8.86 MeV state in 13C and the Hoyle state in 12C. This result is an argument for a similar structure of these states. The unusual result for the compact 3/2– 9.90 MeV state in 13C has been tested by considering its isobar-analog 3/2– 9.48 MeV state in 13N. It has been found that these states have a normal non-increased radius.

This article is devoted to study of isobar-analogue states 1 − in triplet A=14: 14 C- 14 N- 14 O. Previously signs of neutron halo in the 1 − , 6.09 MeV state of 14 C were obtained by two independent groups. In this article we propose to study neighbouring nuclei 14 N and 14 O using the Modified diffraction model (MDM) method and the method of Asymptotic normalization coefficients (ANC). Methods were applied to experimental differential cross sections of 14 C(α,α) 14 C scattering and reactions 13 C( 3 He,d) 14 N and 14 N( 3 He,t) 14 O. MDM and ANC gave practically similar within errors radii for the studied 1 − states: the 6.09 MeV state in 14 C – 2.7±0.1 fm, the 8.06 MeV state in 14 N – 2.7 ± 0.1 fm, the 5.17 MeV state in 14 O – 2.6 ± 0.2 fm. Moreover, the signs of proton halo in the 1 − state of 14 N were obtained for the first time.

The differential cross sections of the B-11(He-3, d)C-12 reaction leading to formation of the 0(+) ground state and the 15.11-MeV 1(+), 16.57-MeV 2(-), and 17.23-MeV 1(-) excited states of C-12 are measured at E-lab = 25 MeV. The analysis of the data is carried out within the coupled-reaction-channels method for the direct proton transfer to the bound and unbound states. The rms radii of the last proton in all states studied are determined. A comparison of the rms radii of the B-12, C-12, and N-12 nuclei in the isobaric analog states (IASs) with isospin T = 1 determined by different methods allows us to arrive at a conclusion that these nuclei in the 1(-) excited states at E-x = 2.62, 17.23, and 1.80 MeV, respectively, possess one-nucleon (neutron or proton) halo structure. The enlarged radii and a large probability of the last neutron to be outside of the range of the interaction potential are also found for the 2(-) states of B-12, C-12, and N-12 at E-x = 1.67, 16.57, and 1.19 MeV, respectively. These IASs also can be regarded as candidates for states with one-nucleon (neutron or proton) halo.

A study of the neutron structure of the ground state of 7 He has been performed by means of registration and analysis of the decay channels of the residual nuclei following absorption of stopped pions. In particular, the reaction 9 Be ( π − , d )X have been investigated where X denotes any system with five neutrons and two protons – the constituencies of a 7 He nucleus. It was shown that the structure of 7 He is determined by correlations of two neutrons in the states 6 He (0 + ), 6 He (2 + ) and one neutron in the shell p 3/2 . The 4 He+3n structure is not manifested in the ground state of 7 He. The obtained results are consistent with the known data on considerable mixture of configurations “ 6 He in its ground and first excited states plus a neutron” in the ground state of 7 He. Comparison of the diffraction components of the differential cross-sections of the charge-exchange reactions ( t , 3 He) measured on 6 Li and 7 Li allowed extracting the radius of particle-unstable nucleus 7 He. The latter occurred to be approximately equal to those of 6 He and 8 He. The obtained result indicates to existence of the halo-like structure in 7 He.

Two independent methods: Asymptotic Normalization Coefficients (ANC) and Modified Diffraction Model (MDM) were applied to new and existing experimental data to search for states with enhanced radii in isobaric analogue states (IAS) of 12 B and 12 N. The ANC analysis of the 11 B(d,p) 12 B reaction at E d = 21.5 MeV has confirmed neutron halo existence for two states of 12 B: 2 − , 1.67 MeV and 1 − , 2.62 MeV [1]. Some new results were obtained for higher excited states: halo-like states were observed for 0 + , 2.72 MeV and 3 − , 3.39 MeV states. It should be mentioned that the last one is unbound state, which is 19 keV above the neutron emission threshold and in both states last neutron has a non-zero orbital momentum (l n =1 and l n =2 correspondingly). We propose to use MDM to study isobaric analogue states of 12 B in the mirror 12 N nucleus and apply it to analyze the ( 3 He,t) reaction data. The existing in the literature data are not completed enough to make definite conclusion about halo in the 2 − and 1 − states of 12 N. This fact simulated us to carry out a new experiment on the 12 C( 3 He,t) 12 N reaction at the end of 2018. The measurements were conducted at the University of Jyväskylä (Finland) using the K130 cyclotron to produce a 3 He beam at E( 3 He)=40 MeV. The differential cross sections of the 12 C( 3 He,t) 12 N reaction were measured in the c.m. angular range 8°–70°. Preliminary results for angular distributions are obtained. MDM analysis of preliminary ( 3 He,t) experimental data is done.

The isobaric analog states with isospin T = 1 in triplet of the A = 14 nuclei: 14C, 14N, and 14O, are studied. The signs of a neutron halo in the 1− (6.09 MeV) state of 14C have been revealed earlier by two groups. We confirm this result and study isobaric analog 1− states of neighboring 14N and 14O nuclei. The differential cross sections for the 14C(α, α)14C* (6.09 MeV, 1−) inelastic scattering, the 13C(3He, d)14N* (8.06 MeV, 1−), and the 14N(3He, t)14O* (5.17 MeV, 1−) reactions are analyzed by two methods: the modified diffraction method and the method of asymptotic normalization coefficients. The rms radii for all three mirror nuclei in the studied 1− states are found almost the same: (2.7 ± 0.1) fm for 14C, (2.67 ± 0.07) fm for 14N, and (2.6 ± 0.2) fm for 14O. The signs of the proton halo in the 1− state of 14N are identified for the first time.