FORMATION OF DEUTERONS IN 16OP COLLISIONS AT 3.25 A GeV/c

Study of the production of light fragments – p, d, t and ³He in the fragmentation of relativistic nuclei is of particular interest, as these fragments, with the inclusive cross section, commensurate with the inelastic cross section of the reaction can be witnessed almost all stages of hadron-nucleus collisions – quasielastic knockout of their primary particle from the nucleus, the Fermi-collapse of the excited residual nucleus and evaporation intermediate weakly excited residual nucleus.

This paper deals with some analysis of studies on the formation of deuterons in the interactions of oxygen nuclei with protons at 3.25 A GeV/c. As is well known [1,р.1388], deuterons can be formed by the Fermi-collapse of the excited residual nucleus oxygen from the decay of the intermediate excited nuclei such as ⁶Li*(α + d), ¹⁰B*(2α + d), ¹⁶O(¹⁴N + d) (in brackets are the decay channels of excited nuclei), the merger of cascade nucleons – protons and neutrons, as well as the destruction of α-cluster (2d) under the influence of the proton target associated with the α-cluster structure of the oxygen nucleus. The experimental data were obtained by the 1 m hydrogen bubble chamber LHE JINR, irradiated by oxygen nuclei with momentum 3.25 A GeV/c in the Dubna synchrophasotron, and are based on a fully measured 8712 inelastic ¹⁶Op events. Methodical features of the experiment associated with the separation of fragments by mass, and the determination of their kinematic characteristics are given in [2,р.497,3,р.336]. The experimental results are compared with the predictions of the cascade-fragmentation evaporation model (CFEM) [4,15р.,5,р.649]. As part CFEM for interactions of light nuclei and nucleons main mechanism of fragments (except nucleons) is the collapse of the excited residual nucleus thermalized after the intranuclear cascade. For light nuclei, such as ¹⁶O evaporative mechanism of formation of fragments in the model is ignored, even including the nucleons. Table 1 shows the experimental and calculated on CFEM average multiplicities and inclusive cross sections for light fragments with mass numbers A ≤ 3.

Table 1

The average multiplicity <n_f> and inclusive cross sections the yield of light fragments ¹H, ²H, ³H and ³He in the experiment and CFEM

Type of fragment	1Н	2Н	3Н	3Не
<nf> (exp)	1.78 ± 0.02	0.331 ± 0.007	0.141 ± 0.005	0.142 ± 0.005
<nf> (CFEM)	1.75 ± 0.01	0.249 ± 0.003	0.108 ± 0.001	0.152 ± 0.002
sin (exp), mbn	594.5 ± 5.5	110.6 ± 2.3	45.0 ± 1.6	45.4 ± 1.6
sin (CFEM), mbn	584.5 ± 2.2	83.2 ± 1.2	34.5 ± 0.7	48.6 ± 0.8

As can be seen from Table 1 average multiplicity (inclusive cross sections) deuterons in the experiment is 1.33 times higher than the estimated average multiplicity (inclusive cross sections) for CFEM. In good agreement with experiment are predicting CFEM nuclei ¹H and ³He. Inclusive cross section for deuteron in the experiment is about 19% cross section of protons and ≈2.4 times the cross sections of the mirror nuclei ³H and ³He. Experimental data for the mirror nuclei ³H and ³He within statistical errors very well coincide with each other. The big difference with the predictions KFIM and experiment is observed also in the formation of nuclei ³H. It also shows that in the model of the ³He isotope has a ≈1.4 times more born than neutron-rich nucleus ³H. This apparently indicates that the model charge proton participates in the formation of the target fragments nucleon, and is not involved in the experiment. Thus, the mechanisms of formation of few-nucleon fragments embedded in axiomatic CFEM are clearly insufficient for a quantitative description of experimental data on the formation of nuclei with mass numbers A≤3.

It is interesting to consider the dependence of the average multiplicity of deuterons on the degree of excitation of the oxygen nucleus. This dependence has been studied in [6,р.51]. As a measure of the degree of excitation of the fragmenting nucleus of oxygen in [6,р.51] was adopted by the total charge (Q) fragments with z ≥ 2 (see. Fig. 1).

Fig. 1 shows that in the model and quantity <n_d> monotonically decreases with increasing Q, that with a decrease of the degree of excitation of the oxygen nucleus. Thus, for values of Q ≥ 5 (in peripheral collisions) the experimental values and the predictions CFEM within statistical errors are the same. Such a coincidence, apparently due primarily to the law of conservation of electric and baryon charges, leading to a decrease of the number of particles that accompany the formation of multiply charged fragments. Along with a decrease in the absolute value of the contribution of the Fermi-collapse occurs also reduce the contribution of other possible mechanisms for the formation of deuterons in the experiment, unrecorded in CFEM. In the Q ≤ 4 experimental values of <n_d> systematically higher than in CFEM. The biggest difference of mean multiplicities of deuterons in the experiment and CFEM observed at the highest levels of excitation fragmenting nucleus oxygen (Q ≤ 2). In such excitations fragmenting nucleus is natural to expect, along with an increase in the contribution of the Fermi-collapse and increasing contributions unrecorded in CFEM fracture mechanisms α-cluster decay of the excited compound nucleus ⁶Li, as well as the growth contribution of formation of deuterons by fusion of protons and neutrons.

In [6,р.51] also investigated the dependence of the mean value of the total momentum of deuterons <p> on the value of Q in the rest frame of the oxygen nucleus (see Fig. 2). Fig. 2 shows that the experimental values of <p>, making within the statistical errors on average 345 MeV/c, almost independent of the value of Q.

Fig. 1. The dependence of the average multiplicity of deuterons on the total charge of fragments with z ≥ 2 in the experiment (●) and CFEM (○).	Fig. 2. Dependence of the mean value of the total momentum of deuterons on the total charge of fragments with z ≥ 2 in the rest frame of the nucleus of oxygen in the experiment (●) and CFEM (○).

To determine the cause of the independence of the average of the total momentum of deuterons on the degree of excitation of the fragmenting nucleus was analyzed momentum spectra of deuterons Group with different values of Q. The momentum spectrum of deuterons was conditionally divided [7,р.1451] into three parts, corresponding to the appearance, mainly the collapse of the Fermi mechanism (0 < p < 275 MeV/c) coalescence (p > 535 MeV/c) and 275 < p < 535 MeV/c – a superposition of the mechanisms of formation of deuterons from the destruction of α-cluster and the collapse of the excited nucleon systems with the structure (α + ²H, 2α + ²H and 3α + ²H). Calculated under these assumptions the share of deuterons in three areas momentum is shown in Fig. 3. There dashed lines show the values of these shares, averaged over Q for each of these mechanisms.

Fig. 3 shows that within the statistical errors experimental values of these shares do not depend on Q. Thus, the independence of the average of the total momentum of deuterons on the degree of excitation of the fragmenting nucleus in our approach is related to the constancy of the relative contributions of the above mechanisms of their formation. For more information about the mechanisms of formation of deuterons interesting to investigate of the multiplicity of other types particles accompanying the birth of deuterons. Consider the associative multiplicity of secondary fragments

Fig. 3. The experimental dependence of the relative contributions of different mechanisms of formation of deuterons on the total charge of fragments with z ≥ 2 in the collapse of a Fermi (■), in the intermediate region with 0.275 ≤ p ≤ 0.535 MeV / c (○) and in the coalescence of the proton and neutron (●).

depending on the presence or absence of the deuteron in the event [7,р.1451]. Table 2 shows the average multiplicities of light fragments (¹H, ³H, ³He and ⁴He) in events with and without deuteron. Also given and calculated data on CFEM.

Table 2

Average multiplicity of light fragments in the events with the formation of the deuteron (n_d ³ 1)and without the deuteron (n_d = 0)

		The fragment type
		1H	3H	3He	4He
nd=0	Exp	1.28±0.02	0.087±0.004	0.088±0.004	0.476±0.011
	CFEM	1.52±0.01	0.096±0.002	0.137±0.003	0.359±0.005
nd³1	Exp	2.24±0.04	0.232±0.011	0.253±0.012	0.806±0.020
	CFEM	2.64±0.03	0.156±0.006	0.211±0.007	0.356±0.010

As can be seen from Table 2, the average multiplicities of light fragments correlated with the presence in the event of the deuteron. In events with the formation of the deuteron multiplicity all considered light fragments larger than in its absence. This fact indicates that the formation of deuterons occurs mainly in the processes with a strong destruction of the original nucleus and of his fragmentation to light few-nucleon fragments. The process looks as if there is an interaction with the α-proton nucleus cluster of oxygen, which then decays into two deuterons, or one of the mirror nuclei (³He or ³H) and the corresponding nucleon. In the second case the deuteron is formed due to the pick-up missing the nucleon. This is supported by the table 3 and fact that in the events with formation of the deuteron, the 4He nucleus appears almost 2 times more likely.  Comparison with CFEM shows that in the experiment the average multiplicity of fragments ¹H and ⁴He in the events of the birth of the deuteron in ≈1.75 times more than in the events without the deuteron. To mirror nuclei ³H, ³He is the difference exceeds 2.7 times. It should be noted that the average of the plurality of nuclei within the statistical error, regardless of the birth event deuteron coincide with each other. In CFEM positive correlation between the average multiplicity of fragments and the presence of the deuteron in the event there are only fragments with mass number A ≤ 3, whereas for 4He within statistical error correlations are absent. We also note that in the model, in contrast to the experiment, matching the average multiplicities for mirror nuclei is observed; the average multiplicity of ³He in ≈1.4 times more than the average multiplicity isotope ³H. CFEM regardless of the deuteron in the event of the birth of overestimates and underestimates the formation of proton nuclei ⁴He that, apparently, due to the neglect of a model a-cluster structure of the nucleus ¹⁶O. Table 3 shows the average multiplicity of fragments with charges 1 ≤ z_f <7 is not separated by mass, depending on the availability of the deuteron in the event [7,р.1451]. Note that the average multiplicity of singly charged fragments is presented without taking into account the multiplicity of deuterons (as trigger particle) deuteron in the event [7,р.1451]. Note that the average multiplicity of singly charged fragments is presented without taking into account the multiplicity deuterons (as trigger particle).

Table 3

The average multiplicity of fragments in events with and without deuteron

nd	The charge of fragment
	1	2	3	4	5	6	7
0	1.37±0.03	0.56±0.01	0.063±0.003	0.035±0.002	0.076±0.003	0.216±0.005	0.247±0.006
³1	2.47±0.04	1.06±0.02	0.12±0.01	0.054±0.005	0.067±0.006	0.126±0.008	0.022±0.003

Here, just as in the Table 2, the correlation between the average multiplicity of fragments and the presence of the deuteron in the event: for fragments with z_f ≤ 4 are positively correlated, and for fragments with 5 ≤ z_f ≤ 7 — negative that seems to be due to conservation of baryon charge and the manifestation of the above-mentioned model a-cluster structure of the nucleus ¹⁶O.

To determine the presence or absence of correlation between the mechanisms of formation of deuterons and other light fragments – protons, tritium and helium-3, consider the average multiplicity of fragments depending on the angle of emission of deuterons [7,р.1451]. Table 4 shows the average multiplicity of light fragments (¹H, ³H, ³He and ⁴He) depending on the angle of departure of the deuteron in the rest of the oxygen nucleus.

Table 4

Average multiplicity of light fragments in events with emission of deuteron back and forward in the rest frame of the nucleus of oxygen

Jd	Type of fragment
	1Н	3H	3He	4He
£900	2.31±0.04	0.215±0.011	0.235±0.012	0.746±0.021
>900	2.35±0.05	0.242±0.019	0.251±0.019	0.753±0.029

The data in Table 4 show that, within the statistic error, the mean multiplicity of the considered fragments do not depend on the angle of emission of the deuteron. That means (given the significant difference in the mechanisms of formation «deuteron-back» and «forward-deuteron») that the formation of associated lung fragments is not related to the manner in which they are born deuterons. In other words, it can be argued that the mechanisms of light fragments independent. A similar result was obtained recently in the analysis of momentum features of light fragments – protons, deuterons, tritium and helium-3 in the events of production and no production α-particles in ¹⁶Op collisions at 3.25 A GeV/c. It has been shown that the average values and widths of the spectra of light fragments on the full and transverse momenta were independent of the presence or absence in the event of α-particles. The dependence of the average multiplicity and kinematic characteristics of the deuteron in the event on the presence of the charged pion [6,р.51]. To avoid the influence of the charge of the proton target on the studied correlations, consider peons from the projectile, ie will deal with the fast (P > 0.5 GeV/c) π+ — and π^—-mesons produced mainly as a result of inelastic charge of one or more nucleons in the nucleus of oxygen during the intranuclear cascade (n ® p +π^—, p ® n + π⁺  Table 5 shows the average multiplicity and average values of the total and the transverse momentum of the deuteron and subject to availability in the event of fast π+ or π^—-meson.

Table 5

The average multiplicity and average values of the total and the transverse momentum of the deuteron in the rest frame of the nucleus of oxygen depending on availability in the event of a charged pion

Value	The presence of charged pions in the event
	nπ+ = 0	nπ+ ≥ 1	nπ– = 0	nπ— ≥ 1
<n>	0.287 ± 0.008	0.412 ± 0.018	0.292 ± 0.007	0.441 ± 0.023
<Р>, МeV/с	343 ± 6	345 ± 9	340 ± 5	358 ± 11
<Р^>, МeV/с	252 ± 5	253 ± 8	250 ± 5	263 ± 9

From Table5 shows thatthe average multiplicityof deuteronsin theevent of productionof charged pionsin≈1.45times more thanin the eventswithout theireducation.Itstilldoes not indicate apossible linkmechanisms of formationof deuteronsandcharged pions. This isapparentlydue to the factthat the eventswith pionimplementedon averageahigher level ofexcitationof the nucleusfragmentingoxygen thantheir formationwithoutevent. Proof ofthe lack of communicationbetween the mechanisms offormationof deuteronsandcharged pionsare independentof mean valuesof full andtransverse momentumof deuteronsfrom thepresence or absence ofthe charged pionin the event.

It is also seen that the average multiplicity and average impulse responses deuteron within the statistical error does not depend on the sign of the charge of fast pions. Thus, the comparison of the experimental and calculated data on the formation of deuterons in ¹⁶Op collisions at 3.25 GeV/c can be concluded that:

— as in the experiment and in CFEM highest average multiplicity deuterons observed at the maximum excitation of the oxygen nucleus and decreases with its decrease. The average multiplicity of deuterons do not depend on the type of mirror nuclei ³H and ³He accompanying the birth of the deuteron, which is a consequence of the deuteron isoscalar nucleus;

— there are positive correlations between the multiplicities of charged pions, and deuterons associated with a high level of nuclear excitation of oxygen in the formation of pions;- Experimental values of the mean total and transverse momenta of deuterons, and their emission angles are independent of the degree of excitation of the fragmenting nucleus of oxygen, which is associated with persistence share of contributions of different mechanisms of their formation; — CFEM qualitatively describing the dependence of the degree of excitation, predicts significantly less than the average total momentum, transverse momentum and emission angle of deuterons. This fact indicates that CFEM, apparently, there is a higher dissipation of excitation energy between nucleons fragments. This leads to the fact that the in model the other fragments, including deuterons, have less kinetic energy, which is observed in the experiment;

— mechanisms of formation of deuterons and other light fragments and charged pions are independent.

The literature

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7. E.H. Bazarov, V. V. Glagolev et al.//Nucl. Phys. V. 68. n. 8. 2005. P. 1451 – 1455.[schema type=»book» name=»THE FORMATION OF DEUTERONS IN 16OP COLLISIONS AT 3.25 A GeV/c» description=»The results of a brief review of experimental studies on the formation of deuterons in 16Op collisions at 3.25 A GeV/c are presented. It is shown that the average multiplicity of deuterons depends on the degree of excitation of the fragmenting nucleus. It is the largest at the maximum excitation of the oxygen nucleus and decreases with its decrease. The mean value of the total, longitudinal and transverse moments of deuterons do not depend on the degree of excitation of the fragmenting nucleus. Formation of deuterons and other light fragments and pions occurs independently. » author=»Bazarov Erkin, Оlimov Kasim, Yuldashev Bekhzod» publisher=»БАСАРАНОВИЧ ЕКАТЕРИНА» pubdate=»2017-01-11″ edition=»ЕВРАЗИЙСКИЙ СОЮЗ УЧЕНЫХ_28.11.15_11(20)» ebook=»yes» ]