a r X i v :n u c l -e x /0305004v 2 4 J u n 2003
Isotopic scaling of heavy projectile residues from the collisions of 25MeV/nucleon
86
Kr with 124Sn,112Sn and 64Ni,58Ni.
G.A.Souliotis,D.V.Shetty,M.Velsky,∗G.Chubarian,L.Trache,A.Keksis,E.Martin,and S.J.Yennello
Cyclotron Institute,Texas A&M University,College Station,TX 77843
(Dated:November 26,2013)
The scaling of the yields of heavy projectile residues from the reactions of 25MeV/nucleon 86Kr projectiles with 124Sn,112Sn and 64Ni,58Ni targets is studied.Isotopically resolved yield distribu-tions of projectile fragments in the range Z=10–36from the reaction pairs were measured with the MARS recoil parator in the angular range 2.7o –5.4o .For the deep inelastic collisions,the velocities of the residues,monotonically decreasing with Z down to Z ≃26–28,are employed to char-acterize the excitation energy.The ratios R 21(N,Z)of the yields of a given fragment (N,Z)from each pair of systems
are found to exhibit isotopic scaling (isoscaling),namely,an exponential dependence on the fragment atomic number Z and neutron number N.The isoscaling is found to occur in the residue Z range corresponding to the maximum obrved excitation energies.The corresponding isoscaling parameters are α=0.43and β=–0.50for the Kr+Sn system and α=0.27and β=–0.34for the Kr+Ni system.For the Kr+Sn system,for which the experimental angular acceptance range lies inside the grazing angle,isoscaling was found to occur for Z ≤26and N ≤34.For heavier fragments from Kr+Sn,the parameters vary monotonically,αdecreasing with Z and βincreasing with N.This variation is found to be related to the evolution towards isospin equilibration and,as such,it can rve as a tracer of the N/Z equilibration process.The prent heavy-residue data extend the obrvation of isotopic scaling from the intermediate mass fragment region to the heavy-residue region.Interestingly,such high-resolution mass spectrometric data can provide important infor-mation on the role of isospin and isospin equilibration in peripheral and mid-peripheral collisions,complementary to that accessible from modern large-acceptance multidetector devices.
PACS numbers:25.70.Mn,25.70.Lm,25.70.Pq
I.INTRODUCTION
The isotopic composition of nuclear reaction products contains important information on the role of the isospin on the reaction dynamics [1].Recently,incread inter-est in the N/Z degree of freedom and its equilibration [2,3,4,5],as well as in the isospin asymmetry depen-dent terms of the nuclear equation of state [6,7]has motivated detailed measurements of the isotopic distri-butions of fragments with Z ≥2[8,9,10,11].Isotopi-cally resolved data in the region Z=2–8have revealed systematic trends,but their N/Z properties are unavoid-ably affected by the decay of the excited primary frag-ments.It has recently been shown [12]that isospin effects can be investigated by comparing the yields of fragments from two similar reactions that differ only in the isospin asymmetry.In this ca,the effect of quential decay of primary fragments can be bypasd to a large extent.It has been revealed that for statistical fragment produc-tion mechanism(s),if two reactions occurring at the same temperature have different isospin asymmetry,the ratio R 21(N,Z)of the yields of a given fragment (N,Z)obtained from the two reactions 2and 1exhibits an exponential dependence on N and Z of the
form:
2
[19].In[19],the fragment yields were measured with ra-diochemical techniques.With mass spectrometric tech-niques,however,apart from isotopically resolved yields, the velocities of the fragments can be obtained with high resolution and can provide information on the excitation energy of the primary fragments.
In the prent work,isotopic scaling is investigated for fragments obtained in high-resolution mass spectromet-ric studies of projectile fragments from the reactions of 25MeV/nucleon86Kr with124,112Sn and64,58Ni targets. Yield ratios of fragments with Z=10–36were obtained and isotopic scaling was investigated.Using the veloci-ties of the residues,the excitation energy of the hot pri-mary fragments was characterized.Finally,the values of the isoscaling parameters were ud to provide isospin information on the hot emitting sources.The paper is or-ganized as follows.In Section II,a brief description of the experimental apparatus,the measurements and the data analysis is given.In Section III,after examiming the av-erage velocity and N/Z characteristics of the fragments, the isotopic scaling of the fragment yields is studied in detail.Finally,conclusions from the prent study are summarized in Section IV.
南京艺术学院研究生招生网II.EXPERIMENTAL METHODS AND DATA
职衔ANALYSIS
The prent study was performed at the Cyclotron In-stitute of Texas A&M University.A25MeV/nucleon 86Kr22+beam from the K500superconducting cyclotron,
with a typical current of∼1pnA,interacted with isotopi-cally enriched targets of124Sn,112Sn(2mg/cm2)and 64Ni,58Ni(4mg/cm2).The reaction products were an-alyzed with the MARS spectrometer[20]offering an an-gular acceptance of9msr and momentum acceptance of 4%.The primary beam struck the target at4.0o rel-ative to the optical axis of the spectrometer.The di-rect beam was collected inside the target chamber on a square Faraday cup lying outside of the angular accep-tance of the spectrometer.Fragments were accepted in the polar angular range2.7o–5.4o.This angular range lies inside the grazing angle of6.5o of the Kr+Sn reac-tions and mostly outside the grazing angle of3.5o of the Kr+Ni reactions at25MeV/nucleon[21].It should be noted that the spectrometer angle tting was chon to optimize the production of very neutron-rich fragments from the Kr+Sn systems who detailed study is reported elwhere[22].An Al foil(1mg/cm2)was ud to ret to equilibrium the ionic charge states of the projectile fragments.MARS optics[20]provid
es one intermedi-ate dispersive image and afinal achromatic image(focal plane).At the focal plane,the fragments were collected in a5×5cm two-element(∆E,E)Si detector telescope. The∆E detector was a position-nsitive Si strip detec-tor of110µm thickness,whereas the E detector was a single-element Si detector of950µm,respectively.Time offlight was measured between two PPACs(parallel plate avalanche counters)positioned at the dispersive image and at the focal plane,respectively,and parated by a distance of13.2m.The PPAC at the dispersive im-age was also X–Y position nsitive and ud to record the position of the fragments.The horizontal position, along with NMR measurements of thefield of the MARS first dipole,was ud to determine the magnetic rigidity, Bρ,of the particles.The reaction products were charac-terized by an event-by-event measurement of energy-loss, residual energy,time offlight,and magnetic rigidity.The respon of the spectrometer/detector system to ions of known atomic number Z,mass number A,ionic charge q and velocity was calibrated using a low intensity86Kr primary beam and other beams at25MeV/nucleon. The determination of the atomic number Z was bad on the energy loss of the particles in the∆E detector [23]and their velocity.The ionic charge q of the parti-cles entering MARS was obtained from the total energy E tot=∆E+E,the velocity and the magnetic rigidity. The measurements of Z and q had resolutions of0.5and 0.4units(FWHM),respectively.Since the ionic charge must be an integer,we assigned integer values of q for each event by putting windows(∆q=0.4)on each peak of the q spectr
um.Using the magnetic rigidity and ve-locity measurement,the mass-to-charge A/q ratio of each ion was obtained with a resolution of0.3%.Combining the q determination with the A/q measurement,the mass A was obtained as:A=q int×A/q(q int is the integer ionic charge)with a resolution(FWHM)of0.6A units. Combination and normalization of the data at the var-ious magnetic rigidity ttings of the spectrometer(in the range1.3–2.0T m),summation over all ionic charge states(with corrections applied for missing charge states [24]),and,finally,normalization for beam current and target thickness,provided fragment yield distributions with respect to Z,A and velocity.Further details of the analysis procedure can be found in[25]and in previous work with heavier beams[26,27,28].The yield distri-butions,summed over velocities,were ud to obtain the yield ratios R21(N,Z)=Y2(N,Z)/Y1(N,Z)employed in the prent isotopic scaling studies.
III.RESULTS AND DISCUSSION
Before embarking on the discussion of the yield ratios and scaling,we willfirst examine the velocity and N/Z characteristics of the reaction products.It is well es-tablished that reactions between massive nuclei around the Fermi energy[18]proceed via a deep inelastic trans-fer mechanism involving substantial nucleon exchange [29,30,31,32].This mechanism is responsible for the creation of highly excited primary fragments that deex-cite to produce the obrved fragments.To obtain infor-
mation about the excitation energy of the primary frag-ments from the prent reactions,we willfirst examine the correlation of the measured velocity with the atomic number.Fig.1prents the average velocities of the
3
fragments as a function of Z.Clod symbols correspond to the reactions with the neutron-rich targets and open symbols to tho with the neutron-poor targets.In this figure,we obrve that for fragments clo to the projec-tile,the velocities are slightly below that of the projectile, corresponding to very peripheral,low-excitation energy events.A monotonic decrea of velocity with decreas-ing Z is obrved,indicative of lower impact parameters, higher momentum transfers,and thus higher excitation
energies.
FIG.1:Average velocity versus atomic number Z correlations for projectile residues from the reactions of (a)86Kr(25MeV/nucleon)with124Sn and112Sn,and(b) 86Kr(25MeV/nucleon)with64Ni and58Ni.Full circles rep-
rent the data with the neutron-rich targets124Sn and64Ni, and open circles tho with the neutron-poor targets112Sn and58Ni.The dashed line(marked“PR”)gives the velocity of the projectile,whereas the arrows indicate the minimum average residue velocities obrved(e text).
For the86Kr+124,112Sn reactions(Fig.1a),the de-scending velocity–Z correlation continues down to
Z∼28; for lower Z’s,the velocity appears to increa with de-creasing Z.The appearance of a minimum velocity for Z∼28can be understood by assuming that the residues originate from primary fragments with a maximum ob-rved excitation energy.Fragments with Z near the projectile down to Z∼28originate from evaporative type of deexcitation which does not modify,on average,the emission direction of the residues.Thus,the residue velocities can provide information on the excitation en-ergy.Residues with lower Z ari,as we will discuss below,from primary fragments undergoing cluster emis-sion and/or multifragmentation and the velocity of the inclusively measured fragments is not monotonically cor-related with the excitation energy,the mass A or the atomic number Z.For the86Kr+64,58Ni reactions,a similar behavior is obrved.However,the decreasing velocity–Z correlation is obrved only down to Z∼32. It should be pointed out that fragments from this re-action were measured mostly outside the grazing angle, so that they correspond to more damped collisions,in such a way that thefinal residues receive a larger re-coil during the deexcitation stage and appear within this angular range.For Z∼30–32,we obrve a minimum ve-locity and for lower Z’s an increa of the velocity with decreasing Z.The average velocities from the reactions with the neutron-rich targets are,within the experimen-tal uncertainties,almost the same as the corresponding from the reactions with the neutron-deficient targets for both pairs of systems.For both reactions,the ascending part of the velocity vs Z correlation for the lower part of the Z range is p
奶油是怎么做成的rimarily due to the combined effect of angle and magnetic rigidity lection.The forward angle range(2.7o–5.4o)lects either the forward or the backward kinematical solution in the moving frame of the quasiprojectile undergoing cluster-emission or multifrag-mentation,whereas the magnetic rigidity range(1.3–2.0 T m)subquently lects the forward solution. Employing the obrved minimum velocities for the Kr+Sn and Kr+Ni reactions and,furthermore,apply-ing two-body kinematics and equal division of excita-tion energy(which is a reasonable assumption for nearly symmetric systems at this energy regime[32,33]),we can estimate an average excitation energy per nucleon for the hot quasiprojectile fragments of E∗/A=2.2±0.1 MeV for both Kr+Sn and Kr+Ni systems.Using the Fermi gas relationship E∗=A
4
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Z for the Kr+Sn reactions (upper panel)and Kr+Ni reactions (lower panel).In the figures,the N/Z val-ues from the reactions involving the neutron-rich tar-gets are shown with full circles and tho involving the neutron-poor targets with open circles.The horizontal dashed line (marked “PR”)reprents the N/Z of the 86
Kr projectile.The thin solid line gives the line of βstability (marked “SL”)
obtained from the relation:Z β=A/(1.98+0.0155A 2/3)[36].Finally,the dotted line reprents the evaporation attractor line (EAL)[37]corresponding to the locus of fragment yields produced by evaporation of neutrons and charged particles from highly excited nuclei clo to stability.(The statistical deexcitation code GEMINI was ud to obtain the posi-tion of the EAL [38].)
FIG.2:Average N/Z versus atomic number Z cor-relations for projectile residues from the reactions of (a)86Kr(25MeV/nucleon)with 124Sn and 112Sn,and (b)86
Kr(25MeV/nucleon)with 64Ni and 58Ni.Full circles rep-rent the data with the neutron-rich targets 124Sn and 64Ni,and open circles tho with the neutron-poor targets 112Sn and 58Ni.The dashed line (marked “PR”)gives the N/Z of the projectile,the solid line (marked “SL”)is the line of sta-bility and the dotted line (marked “EAL”)is the evaporation attractor line [37](e text).
For the Kr+Sn reactions,we obrve that the average N/Z of the fragments clo to the projectile rapidly de-
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creas with deceasing Z down to approximately Z=26–28.For lower Z,the average N/Z appears to be grossly constant with a possible dip around Z=15.The Z value below which the average N/Z of the fragments is roughly constant coincides with the Z value corresponding to the minimum residue velocity,as previously discusd in re-lation to Fig. 1.As expected,the N/Z of the frag-ments from the reactions with the neutron-rich 124Sn are larger than tho from the reactions with the neutron-poor 112Sn target.This difference appears to be largest below Z ∼26,namely clo to the ont of cluster emission and/or multifragmention.In this region,the fragment N/Z deviates from its cour towards or
beyond (to the neutron-poor side of)the stability line and appears to be roughly constant.This feature of multifragmentation of very neutron-rich heavy systems may be exploited in the production of neutron-rich rare isotopes and it will be the topic of a subquent study.
For the Kr+Ni reactions,similar obrvations can be made in Fig.2b.For the reactions,the rapid decrea of N/Z is obrved down to Z=32,corresponding to the Z with the minimum average velocity (Fig.1b).Below Z=32,the N/Z shows a slight decrea and then,below Z=26it becomes roughly constant (again with a dip at Z ∼15,as for Kr+Sn).
Having examined the excitation energy and N/Z char-acteristics of the measured residue data,we turn our dis-cussion to the scaling properties of the fragment yields.According to the equilibrium limit of the grand-canonical enmble,a thermally equilibrated system undergoing statistical decay can be characterized by a primary frag-ment yield with neutron number N,and proton number Z of the form [39,40]:
Y (N,Z )=F (N,Z )exp[B (N,Z )/T ]exp(Nµn /T +Zµp /T )
(1)
杏仁茶的做法where the factor F (N,Z )reprents contributions due to the condary decay from particle stable and unstable states to the final ground state;µn and µp are the neutron and proton chemical potentials;B (N,Z )is the ground state binding energy of the corresponding fragment,and T is the temperature.
A direct comparison of the obrved yield distributions with Eq.1is not possible due to the distortions intro-duced by the quential decay of the primary fragments.However,it has been shown [12],that the ratio of the yields Y 2(N,Z )/Y 1(N,Z )of a given fragment (N,Z)from two different reacting systems,having similar mass and excitation energies,but differing only in N/Z can be ud to obtain information about the excited primary frag-ments.If the main difference between the two systems 2and 1is the isospin,then the binding energy terms in Eq.1cancel out in the ratio Y 2(N,Z )/Y 1(N,Z ).Further-more,if one assumes that the influence of the condary decay on the yields is similar for the two reactions,then a relation of the form
5韩少功
R21(N,Z)=Y2(N,Z)/Y1(N,Z)=C exp(αN+βZ)
(2) can be obtained withα=∆µn/T andβ=∆µp/T, with∆µn and∆µp being the differences in the neutron
and the proton chemical potentials of the fragmenting systems.C is an overall normalization constant.The ratio R21(N,Z)is innsitive to the quential decay and thus it can provide information on the decaying excited primary fragments.
From the prent data,we construct the yield ratio R21(N,Z)using the convention that index2refers to the more neutron-rich system and index1to the less neutron-rich one.Fig.3shows the yield ratios R21(N,Z) as a function of fragment neutron number N for lected isotopes(top panel)and proton number Z for lected isotones(bottom panel)for the Kr+Sn reactions.The different isotopes and isotones considered are shown by alternatingfilled and open symbols for clarity.In Fig. 4,the corresponding ratios for the Kr+Ni reactions are shown.
戴尔biosAs it can be en in the top panels of Figs.3and4,the ratios for each element Z exhibit a remarkable exponen-tial behavior.For each element,an exponential function of the form C exp(αN)wasfitted to the data and also shown in Fig.4for the lected elements.In the mi-log reprentation,the lines for each element are nearly par-allel up to Z∼28for Kr+Sn and up to Z∼34for Kr+Ni (in the latter ca exhausting the whole range of obrved fragments).For heavier fragments from the Kr+Sn sys-tems,thefits to the data show gradual decrea in the slopes with increasing Z of the fragments.An analogous behavior is obrved in the lower panels of Figs.3and 4,where the ratio R21(N,Z)is plotte
d as a function of Z for various isotones.The solid lines correspond to ex-ponentialfits using the expression C exp(βZ).The ratios R21(N,Z)appear to lie along straight lines with nearly similar negative slopesβ,for all isotones up to N∼34for Kr+Sn and N∼44for Kr+Ni(again,in the latter ca covering the whole fragment range).For larger N from Kr+Sn,the slopesβincrea with increasing N of the fragments.The positive slopes in the upper panels of Figs.3and4indicate that neutron-rich fragments are more efficiently produced,as expected,from the more neutron-rich systems.Similarly,the negative slopes in the bottom panels of thefigures indicate that proton-rich fragments are more efficiently produced from the more proton-rich systems.
In Fig.5,we prent the slope parametersα(upper panel)andβ(lower panel)of the exponentialfits(ob-tained as described for Figs.3and4)as a function of Z and N.For the Kr+Sn reactions,the slope parameter αis roughly constant with an average value of0.43in the range Z=10–26and then decreas for Z>26.Simi-larly,the parameterβappears to be nearly constant at an average value of–0.50up to N∼34and ri for N>34. Conquently,for the Kr+Sn systems under the
prent experimental conditions,isoscaling(as defined in[12])FIG.3:Yield ratios R21(N,Z)=Y2(N,Z)/Y1(N,Z)of pro-jectile residues from the reactions of86Kr(25MeV/nucleon) with124,
112Sn(a)with respect to N for the Z’s indicated,and (b)with respect to Z for the N’s indicated.The data are given by alternatingfilled and open circles,whereas the lines are exponentialfits(e text).
holds up to Z∼26and N∼34.This fragment range cor-responds to primary events with the maximum obrved excitation energy of2.2MeV/nucleon and temperature of5.3MeV,as estimated previously.For the Kr+Ni re-actions,the slope parameterαappears to be constant in the whole range Z=10–36at an average valueα=0.27. Similarly,the parameterβremains constant at an aver-age value of–0.34in the whole N range.In the ca of the Kr+Ni systems under the prent experimental con-ditions(obrvation outside the grazing angle),isoscaling holds in the whole range of obrved fragments,corre-sponding to primary events having on average excitation energy of2.2MeV/nucleon and temperature of5.3MeV. The near constancy of the isoscaling parametersαandβ(except for near-projectile fragments for the Kr+Sn sys-tem)corroborates the statistical nature of the fragment production under the excitation energy and temperature values extracted from the minimum obrved residue ve-locities.In general,the extracted isoscaling parameters αandβare in agreement with the corresponding values
