Quasi-elastic scattering of proton with 1 GeV energy on eight-nucleon cluster inside nucleus
O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky, V. A. Andreev, G. V. Fedotov, G. E. Gavrilov, A. A. Izotov, N. G. Kozlenko, P. V. Kravchenko, V. I. Murzin, D. V. Novinskiy, A. V. Shvedchikov, V. A. Stepanov, A. A. Zhdanov
aa r X i v : . [ nu c l - e x ] F e b QUASI-ELASTIC SCATTERING OF PROTON WITH 1 GEVENERGY ON EIGHT-NUCLEON CLUSTER INSIDE NUCLEUSO.V. Miklukho, A.Yu. Kisselev, G.M. Amalsky, V.A. Andreev,G.V. Fedotov, G.E. Gavrilov, A.A. Izotov, N.G. Kozlenko,P.V. Kravchenko, V.I. Murzin, D.V. Novinskiy, A.V. Shvedchikov,V.A. Stepanov, and A.A. Zhdanov
B.P. Konstantinov Petersburg Nuclear Physics Institute, National ResearchCentre Kurchatov Institute, Gatchina, 188300 Russia
Available data on the polarization of the secondary proton (as a function ofits momentum K ) in the inelastic ( p, p ′ ) reactions with the Be, C, and Canuclei and differential cross section data (the momentum distributions) for thereactions at the initial proton energy 1 GeV and scattering angles Θ=21 ◦ andΘ=24.5 ◦ were analysed in a range of the high momenta K close to the momen-tum corresponding to the proton elastic scattering off the investigated nucleus.A structure in the polarization and momentum distribution data at the highmomenum K , related probably to quasi-elastic scattering off a Be-like nucleoncluster inside the nuclei, was observed.PACS numbers: 13.85.Hd, 24.70.+s, 25.40.Ep, 29.30.-h
Comments:
14 pages, 11 figures.
Category:
Nuclear Experiment (nucl–ex) pectrometer MAPProton beamS2 Q2D C TSM1−M3Q1S1PC3PC2PC1PC4 A PC1’PC4’
Figure 1:
The experimental setup. TS is the target of the MAP spectrometer; Q1 ÷ Q2are the magnetic quadrupoles; D is the dipole magnet; C1 is the collimator; S1 ÷ S2and M1 ÷ M3 are the scintillation counters; PC1 ÷ PC4, PC1 ′ , PC4 ′ and A are theproportional chambers and the carbon analyzer of the MAP polarimeter, respectively. This work is a part of the experimental program in the framework of whichthe effects of nucleon clusterization in nuclear matter is studied in the inclusive( p, p ′ ) experiments at the PNPI synchrocyclotron with the 1 GeV proton beam[1, 2, 3, 4, 5, 6, 7].The general layout of the experimental setup is presented in Fig. 1.The proton beam was focused onto the target TS of the magnetic spectrometerMAP. The beam intensity was monitored by the scintillation telescope M1, M2,M3. The spectrometer was used to measure the momenta of the secondary protonsfrom the inclusive ( p, p ′ ) reaction as well as their polarization. The momentum ofthe scattered proton ( K ) was determined using the coordinate information fromthe proportional chamber PC2-X. The momentum resolution of the spectrometer( ± + excited level in the ( p, p ′ ) reaction with the C nucleus at the scatteringangle 21 ◦ under investigation (Fig. 2) [3]. In this measurement we also observeda peak (Fig. 2) which was first identified as the 1 + excited level predicted in[8]. The polarization of secondary protons in the ( p, p ′ ) reaction was foundfrom an azimuthal asymmetry of the proton scattering off the carbon analyzer A,using the track information from the proportional chambers (PC1 ÷ P4 and PC1 ′ ,PC4 ′ ) of the polarimeter. The main parameters of the MAP spectrometer andthe polarimeter are given in [3].Earlier, the secondary proton polarization ( P ) and its momentum distribution(differential cross section σ incl = d σd Ω dK ) in the inelastic ( p, p ′ ) reaction with nucleuswere measured at the scattered angle of Θ=21 ◦ . The nuclei Be [5], C [3] , Si2 (15.11 MeV) = 21 o Θ (4.43 MeV)Background level C scattering , MeV/c K C( p, p’ Elastic − p ) XN Figure 2:
Momentum distribution in the inclusive reaction C( p, p ′ )X at a scatteringangle Θ=21 ◦ [3]. [4], Ca [3], Fe [4], and Zr [5] were investigated. The structure in theseexperimental data was observed that possibly related to quasi-elastic scatteringin the momentum intervals II, III, and IV on two-nucleon ( H), three-nucleon( He, H), and four-nucleon ( He) correlations, respectively [9, 10].Recently the momentum distributions of the secondary protons in the ( p, p ′ )reaction with nuclei Be, C, and Ca were measured at the scattering angleof Θ=24.5 ◦ . The measurements were done in the range of high momenta of thescattered proton only. The measured momentum distribution of the secondary proton produced in thereaction Be( p, p ′ )X at the angle of Θ = 21 ◦ with the momentum K and itspolarization are presented in Fig. 3 and Fig. 4, respectively [5].In Fig. 3, there is a wide peak in the momentum distribution with energy ω = ω = 26 MeV transferred into the nucleus. What is the nature of this peak?Each momentum interval II, III, and IV (Fig. 4) is related to the dominance ofquasi-elastic scattering Be( p, p ′ NC) X ( X is a residual nucleus of the reaction)on a certain low-nucleon correlation (NC). These reactiions are: Be( p, p ′ H) Lifor the interval II; Be( p, p ′ He) He and Be( p, p ′ H) Li for the interval III;3
III
Background level 16201600 1640 1660 K , MeV/ c Θ = 21 ο N Be( p, p’ ) X at 1 GeV Be p − Elastic = 26 MeV ω ω = 0 MeV ω = 9.7 MeV IV Figure 3:
Momentum distribution of the protons scattered at an angle Θ = 21 ◦ in theinclusive reaction Be( p, p ′ )X. K is the secondary proton momentum. A difference ofthe secondary proton energy calculated for the elastic proton scattering off the nucleusunder investigation and measured in the experiment is signified by ω . The momentuminterval VIII (IV) corresponds to quasi-elastic scattering on a Be - like (a He - like)nucleon cluster. Be( p, p ′ He) He for the interval IV. A high-momentum region, that begins closeto the end of the IV range (Figs. 3, 4) corresponds mainly to quasi-elastic scat-tering on the residual nuclei X from the reactions Be( p, p ′ NC) X noted above: Be( p, p ′ Li) H, Be( p, p ′ He) He, Be( p, p ′ Li) H, and Be( p, p ′ He) He.This overlap of the momentum intervals for the reaction Be( p, p ′ He) He (in-terval IV) and, mainly, for the reactions Be( p, p ′ Li) H and Be( p, p ′ He) Hewith the light nucleus, Be, is due to relatively close masses of the correlationsand residual nuclei.In Fig. 3, there is a second rather wide peak in the momentum distributionwith energy ω = ω = 9.7 MeV transferred into the Be nucleus. The kinematiccalculation shows that this peak possibly corresponds to quasi-elastic scatteringon a Be - like nucleon cluster in the momentum interval VIII. The detectionof this peak supports a theoretical model of the Be nucleus, within which thenucleus consists of a solid nucleon core ( Be - like nucleon cluster) and an externalneutron weakly bound to this core [11]. A value of the measured polarization ofthe secondary protons produced at the scattering angle Θ = 21 ◦ in the momentuminterval VIII is given in Fig. 4.The measured momentum distribution of the secondary protons produced inthe reaction Be( p, p ′ ) X at the scattering angle Θ = 24.5 ◦ is shown in Fig. 5.4 MeV/ Be( ) at 1 GeV Θ = 21 | | | | II P p, p’ X III K pN ω ω cK ω = 0 MeV ω = 9.7 MeV ω ω = 26 MeV IV VIII
Quasi−elastic scattering on a Be − like nucleon cluster
Interval VIII : K ~ 1650 − 1660 MeV/ c Polarization :
K K K
Figure 4:
Polarization P of the protons scattered at an angle Θ = 21 ◦ (black squares)in the inclusive reaction Be( p, p ′ ) X versus the secondary proton momentum K . Theempty square corresponds to the polarization in the elastic p - He scattering [12]. Thedotted lines cover the K intervals II, III, and IV corresponding to quasi-elastic scatteringon two-nucleon ( H), three-nucleon ( He, H), and four-nucleon ( He) correlations,respectively. The calculated secondary proton momenta for the maxima of the quasi-elastic peaks in the Be( p, p ′ NC) X reaction with the corresponding nucleon correlation(NC) are designated as K , K , and K . A narrow momentum interval VIII correspondsto the quasi-elastic proton scattering on a Be-like nucleon cluster. Momentum K pN corresponds to the maximum of the quasi-elastic peak in the proton scattering offnuclear nucleons. K, MeV/c9Be( p, p’
Θ = 24.5ο ω = 35 MeV ω = 10.6 MeV ω = 0 MeV p − Elastic BescatteringBackground level N IV VIII ) X Figure 5:
Momentum distribution of the protons scattered at an angle Θ = 24.5 ◦ in theinclusive reaction Be( p, p ′ ) X . K is the secondary proton momentum. A difference ofthe secondary proton energy calculated for the elastic proton scattering off the nucleusunder investigation and measured in the experiment is signified by ω . The momentuminterval VIII (IV) corresponds to quasi-elastic scattering on a Be - like (a He - like)nucleon cluster.
This distribution (Fig. 5) likes to that shown in Fig. 3. There are also twowide peaks corresponding to the transfered energy ω = ω = 35 MeV and ω = ω = 10.6 MeV. The peak at the ω = ω is possibly related to quasi-elastic scatteringon a Be - like nucleon cluster.In Fig. 6, the measured momentum distribution of the secondary protonsproduced in the reaction with carbon nucleus C( p, p ′ ) X at the scattering angleΘ = 21 ◦ is shown. A stepwise similar drop in the momentum distribution isobserved, which corresponds possibly to quasi-elastic scattering on a nucleoncluster (NCL) inside the C nucleus ( Be, B, B, and Be) in a reaction C( p , p ′ NCL)NC. Where NC is corresponding few-nucleon correlation ( He, H, H,and He). This momentum distribution at the K momentum greater than 1640MeV/ c is shown in Fig. 7. According to kinematic calculations, a rather narrowpeak at K = 1658 MeV/ c (at the ω = 14.9 MeV) corresponds likely to quasi-elastic scattering C( p, p ′ Be) He on a Be - like nucleon cluster inside thecarbon nucleus. A value of the measured polarization of the secondary protonsin the quasi-elastic scattering on this cluster is given in Fig. 8.6 K , MeV/ c ) X Θ p, p’ = 21 N C( p − C elastic scattering ω o = 0 MeV He Be) C( p, p’ ω p, p’ He p, p’ ) Be, He
84 9
BeBe BC(C(C( p, p’ )H p, p’ HC( ) B BBL
Figure 6:
Momentum distribution of the protons scattered at an angle Θ = 21 ◦ in theinclusive reaction C( p, p ′ ) X . K is the secondary proton momentum. Dashed verticalline at the K = 1610 MeV/ c indicates the region of large K , where effective registrationof the secondary protons is carried out. In the upper right corner of the figure, reactionsare presented in which the proton scattering by few-nucleon correlations ( H, H, He,and He) was studied. Vertical arrows point to the calculated maxima of quasi-elasticpeaks in scattering by residual nuclei ( Be, Be, B, and B) in the reactions notedabove. A difference of the secondary proton energy calculated for the elastic protonscattering off the nucleus under investigation and measured in the experiment is signi-fied by ω . Moreover ω = ω and ω = ω correspond to elastic scattering on the nucleusunder study and quasi-elastic scattering on a Be-like nucleon cluster inside the Cnucleus. BL means background level. + = 21 o Θ (4.43 MeV)Background level C scattering p,p’ p, p’ Elastic − p )C( C( X K , MeV/ cN ωω = 0 MeV= 14.9 MeV He )Be Figure 7:
Momentum distribution of the protons scattered at an angle Θ = 21 ◦ in theinclusive reaction C( p, p ′ ) X . K is the secondary proton momentum. A difference ofthe secondary proton energy calculated for the elastic proton scattering off the nucleusunder investigation and measured in the experiment is signified by ω . Moreover ω = ω and ω = ω correspond to elastic scattering on the nucleus under study and quasi-elasticscattering on a Be-like nucleon cluster inside the C nucleus.
The measured momentum distribution of the secondary protons produced inthe reaction with carbon nucleus C( p, p ′ ) X at the scattering angle Θ = 24.5 ◦ ispresented in Fig. 9. This distribution is similar to the momentum distribution atthe scattering angle Θ = 21 ◦ (Fig. 6). A stepwise similar drop in the momentumdistribution is also observed, which corresponds possibly to quasi-elastic scatter-ing on a nucleon cluster (NCL) inside the C nucleus ( Be, B, B, and Be)in a reaction C( p , p ′ NCL)NC. Where NC is corresponding few-nucleon corre-lation ( He, H, H, and He). According to kinematic calculations, a peak atthe transferred energy ω = 18.4 MeV to nucleus under investigation correspondslikely to quasi-elastic scattering C( p , p ′ Be) He on a Be - like nucleon clusterinside the carbon nucleus.When studying the ( p, p ′ ) reaction with Ca nucleus at a scattering angleof the secondary protons of 21 ◦ , no structure was found in their momentumdistribution, that could indicates proton scattering by a Be-like nucleon clusterinside this nucleus. However, at a scattering angle of 24.5 ◦ (Fig. 10), a bump inthe momentum distribution is observed, that, according to kinematic calculations,can be associated with scattering by a Be-like nucleon cluster inside the Canucleus. In Fig. 11 corresponding to scattering at an angle of 21 ◦ on the Canucleus, an estimate of the polarization in quasi-elastic scattering on this clusteris given. 8 MeV/ ) at 1 GeV Θ = 21 | ||| KK K K K cp, p’ X P P K C( IIIII IV Be DWIA ω Be − like nucleon cluster ω ~ 1658 MeV/ Quasi−elastic scattering on a Lower estimate of polarization measurement: c = 0.384 + − 0.024 pN * Figure 8:
Polarization P of the protons scattered at an angle Θ = 21 ◦ (black squares)in the inclusive reaction C( p, p ′ ) X versus the secondary proton momentum K [3,7]. The empty square corresponds to the polarization in the elastic p − He scattering[12]. The dotted lines cover the K intervals II, III, and IV corresponding to quasi-elastic scattering on two-nucleon ( H), three-nucleon ( He, H), and four-nucleon ( He)correlations, respectively. The calculated secondary proton momenta for the maxima ofthe quasi-elastic peaks in the C( p, p ′ NC) X reaction with the corresponding nucleoncorrelation (NC) are designated as K , K , and K . Momentum K pN corresponds tothe maximum of the quasi-elastic peak in the proton scattering off nuclear nucleons.The dashed curve presents the polarization calculated in the framework of a spin-dependent Distorted Wave Impulse Approximation taking into account the relativisticdistortion of the nucleon spinor in nuclear medium (DWIA*) [3]. In this approach theproton scattering off the independent nuclear nucleons was taken into account only.The energy ω = 14.9 MeV transferred to the C nucleus (Fig. 7) corresponds toquasi-elastic scattering on a Be-like nucleon cluster inside the nucleus. K , MeV/
2B +BBe, cN ) p, p’ X )C( p, p’ He) C( p, p’ He)C( p, p’ )HH C( p, p’ BBBeBe C( Θ = 24.5 p − ω C( p, p’ Be)
He8 Be ω = 18.4 MeV1 C elastic scattering BL Figure 9:
Momentum distribution of the protons scattered at an angle Θ = 24.5 ◦ in theinclusive reaction C( p, p ′ ) X . K is the secondary proton momentum. Dashed verticalline at the K = 1610 MeV/ c indicates the region of large K , where effective registrationof the secondary protons is carried out. In the upper right corner of the figure, reactionsare presented in which the proton scattering by few-nucleon correlations ( H, H, He,and He) was studied. Vertical arrows point to the calculated maxima of quasi-elasticpeaks in scattering by residual nuclei ( Be, Be, B, and B) in the reactions notedabove. A difference of the secondary proton energy calculated for the elastic protonscattering off the nucleus under investigation and measured in the experiment is signi-fied by ω . Moreover ω = ω and ω = ω correspond to elastic scattering on the nucleusunder study and quasi-elastic scattering on a Be-like nucleon cluster inside the Cnucleus. BL means background level. K , MeV/ c p, p’ ) X p − = 0 MeV Ca( Θ = 24.5 N Be Ca( Be) p, p’ S ω ω = 40.5 MeVBL Ca elastic scattering Figure 10:
Momentum distribution of the protons scattered at an angle Θ = 24.5 ◦ inthe inclusive reaction Ca( p, p ′ ) X . K is the secondary proton momentum. Dashedvertical line at the K = 1610 MeV/ c indicates the region of large K , where effectiveregistration of the secondary protons is carried out. Vertical arrow points to the calcu-lated maximum of quasi-elastic peak in the scattering Ca( p, p ′ Be) S by a Be-likenucleon cluster inside the Ca nucleus. A difference of the secondary proton energycalculated for the elastic proton scattering off the nucleus under investigation and mea-sured in the experiment is signified by ω . Moreover ω = ω and ω = ω correspondto elastic scattering on the Ca nucleus and quasi-elastic scattering on the Be-likenucleon cluster. BL means background level. MeV/ ) at 1 GeV Θ = 21 | |||| * K KK KK K p,p’
Ca( X K c P P II IVIII ω Be Quasi−elastic scattering on a Be − like nucleon cluster ω = 33.7 MeV, Polarization value: ~ 1650 MeV/ = 0.397 + − 0.022 c DWIA pN * Figure 11:
Polarization P of the protons scattered at an angle Θ = 21 ◦ (black squares)in the inclusive reaction Ca( p, p ′ ) X versus the secondary proton momentum K [3].The empty square corresponds to the polarization in the elastic p − He scattering [12].The dotted lines cover the K intervals II, III, and IV corresponding to quasi-elasticscattering on two-nucleon ( H), three-nucleon ( He, H), and four-nucleon ( He) cor-relations, respectively. The calculated secondary proton momenta for the maxima ofthe quasi-elastic peaks in the C( p, p ′ NC) X reaction with the corresponding nucleoncorrelation (NC) are designated as K , K ( K ∗ ), and K . Momentum K pN correspondsto the maximum of the quasi-elastic peak in the proton scattering off nuclear nucleons.The dashed curve presents the polarization calculated in the framework of a spin-dependent Distorted Wave Impulse Approximation taking into account the relativisticdistortion of the nucleon spinor in nuclear medium (DWIA*) [3]. In this approach theproton scattering off the independent nuclear nucleons was taken into account only.The energy ω = 33.7 MeV transferred to the Ca nucleus corresponds to quasi-elasticscattering on a Be-like nucleon cluster inside the nucleus. Summary
A kinematic analysis of momentum distributions of the secondary protons in aninclusive ( p, p ′ ) reaction with Be, C, and Ca nuclei at an energy of 1 GeV andscattering angles of 21 ◦ and 24.5 ◦ is carried out. In a range of the high momentaclose to the momentum corresponding to the proton elastic scattering off thenucleus under study, the analysis indicates quasi-elastic scattering by a Be-likenucleon cluster inside the nucleus. This observation supports a theoretical modelof Be nucleus, within which the nucleus consists of a solid nucleon core and anexternal neutron weakly bound to this core.For the scattering angle Θ = 21 ◦ , an estimate of the secondary proton polar-ization in quasi-elastic scattering on a Be-like nucleon cluster is given for nucleiunder investigation.The authors are grateful to the PNPI 1 GeV proton accelerator staff for thestable beam operation. 13 eferences [1] O. V. Miklukho, G. M. Amalsky, V. A. Andreev et al., arXiv:1103.6113v1[nucl-ex] (2011).[2] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., JETP Letters ,11 (2015).[3] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., Phys. Atom. Nucl. , 299 (2017).[4] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., Phys. Atom. Nucl. , 320 (2018).[5] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., Phys. Atom. Nucl. , 431 (2020).[6] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., JETP Letters ,69 (2017).[7] O. V. Miklukho, A. Yu. Kisselev, G. M. Amalsky et al., J. Phys.: Conf. Ser. , 012013 (2017).[8] R. D. Viollier, ANNALS OF PHYSICS , 335 (1975).[9] D. I. Blokhintsev, Zh. Eksp. Teor. Fiz. , 1295 (1957).[10] K. S. Egiyan et al., Phys. Rev. Lett. , 082501 (2006).[11] V. Chavchanidze, ”On the theory of the beryllium nucleus”, Russian sci-entific journal: Uspekhi Fizicheskikh Nauk (UFN) , 106 - 119 (1951) [inRussian].[12] O. V. Miklukho, G. M. Amalsky, V. A. Andreev et al., Phys. Atom. Nucl.69