- Email: [email protected]
Non-equilibrium particle emission in heavy-ion fusion-evaporation reactions
Nuclear Instruments and Methods in Physics Research BlO/ll North-Holland, Amsterdam
NON-~~~~ REACIIONS Charles Department
441
(1985) 441-453
PARTICLE EMISSION IN HEAVY-ION ~SION-EVANSTON
F. MAGUIRE of
Physics and Astronomy, Vanderbiiit University, Nashvilie, TN 37.235, USA
Non-equilibrium particle emission occurxing in heavy-ion fusion-evaporation reactions is analyzed in terms of the moving source model. Different projectile-target combinations are. seen to give different source characteristics depending upon the particle being detected. Non-equilibrium particle production in a heavy projectile reaction, **Si+ *Ca, is practically non-existent even at a relatively high projectile v&city aboye the koulomb barrier.
1. inbwhrction
For projectile energies having only a few MeV per nucleon above the Coulomb barrier in nucleus-nucleus collisions, the light-particle (neutron, proton, alpha) emission spectra appear to be well understood in terms of the statistical decay of temperature equilibrated systems. This is true for complete fusion compound nucleus formation [l-3] as well as for deep-inelastic collisions [4-61. At a certain threshold, perhaps 5 MeV per nucleon above the barrier, non-equilibrium components have been identified in the particle emission spectra for a wide variety of experiments [7-lo]. It is tempting to think of the origin of these energetic particles in thermodynamic concepts. That is the thermal conductivity limit of nuclear matter has been breached and too much kinetic energy has to be dissipated too fast at the collision boundary. More specifically, a hot spot [xl-121 of nuclear matter develops, consisting of a restricted subset of the colliding nucieons and responsible for non-equilibrium particle production. On the other hand, these non-equilibrium features may reflect new facets of the nucl~s-nucleus collision as the mean-field induced phenomena receive competition from nucleon-nucleon interactions at the higher projectile velocities with reduced Pauli blocking. In any event the study of the emission of energetic light particles will illuminate the dynamics of the heavy-ion reaction process at its earliest stages. The subject of this paper will focus on energetic particle emission in fusion-evaporation reactions which will complement the results already in hand from fusion-fission reactions and deep-inelastic studies. 2. shtgles aystematiea A seminal earlier inclusive experiment [13] measured the proton, deuteron, Won, and alpha particle spectra 016%583X/85/$03.30 0 Blsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
produced in 160 induced reactions at 5 to 16 MeV per nucleon above the barrier on targets of mass A = 27 to A = 197. A typical result is depicted in fig 1, which shows the proton singles spectra at 215 and 310 MeV for the target “Zr. These spectr a display exponentially decreasing structureless tails going out to 3 or 4 times @teincident beam velocity of 13 or 19 MeV per nucleon. The slopes change with angle, becoming steeper at more backward angles suggesting some source motion is required. In this experiment a low energy cut-off of 12 MeV (Z=l), or 30 MeV (Z-2), was in place so the compound nucleus evaporation peak and roll-off at low energy are not visible. The spectra can be fitted in general by a moving Maxwellian source, characterized by its own temperature T and a velocity u paraBe to the beam velocity. Transforming to the lab and including Coulomb repulsion from the target, one obtains the double differential cross section as:
where EC = Coulomb repulsion energy after emission, E, = source “velocity” (MeV/amu), 8 = lab detection angle, T = source temperature, N, = source strength, energy and angle integrated yield: CJ= 2No(prT)‘/‘. The temperature T and the source velocity u parameters are extracted according to the fits of this function to the data. The smooth trends of these parameters are illustrated in fig. 2 from this experiment. One sees for the two heavier targets measured that both the temperature and the source velocity appear to track linearly with the projectile velocity above the barrier, and both parameters disagree with the values expected from just compound nucleus production alone. In particuhu, the source velocity is about half the beam velocity, indicating in this analysis that only a partial fraction of the III. NUCLEAR PHYSICS/ASTROPHYSICS
C.F. Maguire / Non -equilibrium particle emission
442
160+9OZr+p+X
l
EXPERIMENT
- MOVING
SOURCE
10’3 10’2
310 _
I_
-
T
=
9.B
Er
=
5.0
=
5.73
MeV MeV MeV
MeV
Fig. 1. Inclusive proton spectra of I60 on 90Zr for projectile energies of 215 and 310 MeV (from ref. 13).
The curves through the data points 80
ENERGY
total
[MeV)
nucleus is interacting to produce the energetic light particles. Of course, one should not push the inclusive measurements too hard since there can clearly be many effects contributing to the measured particle spectra. Detailed questions as to the origin of the energetic particles can only be answered by coincidence studies. An innovative technique in this regard was the study [14] of particle correlations in fusion-fission reactions. The fission fragments are detected in coincidence and their opening angle determines the degree of linear momentum transferred in the collision (fig. 3). Opening angles near 180” signify peripheral type collisions while smaller opening angles reflect central collisions corresponding to near complete fusion of the projectile and the target. Fig. 4 shows the results [15] of neutron spectra in coincidence with (single) fission fragments for 160 on 238U at 310 MeV. Two components in the spectra are seen, coming from compound nucleus evaporation of fission fragment decay, and from neuiron emission before equilibration has occurred. The origin of the light particles is seen in the proton emis-
160 are moving source model predictions as described in the text.
sion channel, shown in fig. 5, where one now also has information on the opening angle of the fission fragments [16]. One infers conclusively from these coincidence data that the intermediate angle yields come almost completely from the full momentum transfer, central collisions, equivalently the compound nucleus. On lighter mass targets, for which the compound nucleus fission barriers are much higher, similar information can be obtained by gating on the fusion-evaporation residues whose velocities and mass give an unambiguous signal of large momentum transfer.
3. Summed fusion-evaporation
coincidence data
A systematic measurement [17] of non-equilibrium neutron emission has been made for “(2, 13C, and *ONe projectiles at specific energies on selected targets, all leading to the same compound nucleus, “‘Yb, at comparable excitation energies. Neutron spectra were collected in coincidence with fusion-evaporation residues detected at a forward angle. As was the case for the
C. F. Maguire / Non -equilibrium pariicle emission
8.
6-
160+23*u
MOVING SOURCE PARAMETERS INCLUSIVE PROTONS
310
l-
+
n+f
1
MeV
0.
0) 10‘
z E
443
4-
10’ 7 ‘z u-l ;
‘O’
f 10‘
.a-
b) c:
10’
.06 % z’
10’
\. C-F -0
10’
10’
lo-
Fig. 2. Systematics of the moving source model parameters derived in ref. 13. According to this analysis, the source of the high energy protons was not the compound nucleus, but a higher temperature region moving at near the nucleon-nucleon collision velocity.
10’
ENERGY
[MeV)
Fig. 4. Neutron spectra in coincidence with fission fragments for the reaction of 1sO+23sU at 310 MeV. Note the two components, low and high temperature, detection angles (from ref. 15).
visible at all neutron
neutrons shown in fig. 3, the evaporation residue gated neutrons here displayed two components, one with a low temperature obviously coming from the compound nucleus, and the second of a much higher temperature and concentrated in yield at forward angles. The results of this study are summarized in figs. 6-8, in terms of the non-equilibrium neutron multiplicity, and the temperature and velocity of the apparent source of these
Fig. 3. Plot of the opening angIe between coincident fission fragments, showing the division between peripheral collisions (small linear momentum transfer, larger opening angles) and central collisions (near full momentum transfer, smaller opening angles). The deep-inelastic projectile-like fragments are seen to be associated with the peripheral collisions, as expected, (from ref. 14).
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C. F. Maguire
/
Non -equilibrium
parricle emission
I ‘sO+238U-X
4
:
.
:::::t:::::: x=t
Et>15
lo-2
lO-3 7
l
.
0 Sum A 0 Cantrol A Peripheral
O.lr
:
1
0 0
.
c : 10-4 r
MeV
.
clo-5-::::::t+:::; 0
-0
A
.
10-3
T
rn’@
8
.
TL v,
315
0
.
lo-2/
f,
b A
.
4 .a
a @ . .
‘:
8
. ‘@ *
0 A 8 ‘5
10-4r
. . .,,.,,.,,.,,,. 30 60
90
-!
. .,,,.I,.,,,,., 120 0 30 60 8, K!EGREES)
. 90
120
Fig. 5. Charged light particle spectra measured in coincidence with fission fragments for the reaction ‘60+23sU more backward angle yields are. seen to be almost exclusively associated with central collisions (from ref. 16).
at 315 MeV. The
energetic
mzutrons. When plotted as a function of the projectile energy per nucleon above the barrier, the non-equilibrium multiplicity appears to increase linearly, and independently of the projectile being considered. The velocity trend is in line with the predictions of the Boltzmann Master Equation model [18] (BME) but that model predicts, incorrectly, very different multiplicities as a function of projectile mass. The temperature of the non-equilibrium neutrons (fig. 7) appears nor to depend strongly on the projectile velocity in contradiction to the inclusive charged particle measurements discussed above [13] and also in marked contrast to the predictions of the BME model. The pattern of constant temperature values also is inconsistent with the increasing temperature values predicted by a derivation [17] based on the hot-spot picture. The source velocities
01 0
’
’
4
’
’
4
’
( EC,,,-Vc I/&
’s
’
’ e
’
’ ’ IO
N'eV~nuc~eon)
I2
Fig. 6. Non-equilibrium neutron multiplicity for 12C, 13C, and “Ne induced fusion-evaporation reactions all leading to 170Yb. The non-equilibrium multiplicities are plotted as function of the c.m. energy above the Coulomb barrier per nucleon. The open circles are 12C, the full circles are “C, and the triangles mNe data points. The straight lines A, B and C represent BME fits (see text) for 12C, 13C and 20Ne, respectively (from rcf 17).
C. F. Maguire
/
Non -equilibrium
445
particle emission
204
MeV ‘%+=Nb
c-a
e,, =-21’
5m
e-
._
2-
-80
0
80
8, (lab1 MegI
01 0
’
’
’
2
’
’
’
’
’
’
’
Y)
4 6 0 (E c,_.‘vc ) /#a(MeVhluckan~
1
’
t2
Fig. 7. As in fig. 6, expect the non-equilibrium neutron source temperature is plotted. The solid lines are the BME model predictions, the dashed line is the result m-portedin ref. 13, and the dashed-dotted line is a hot-spot model fit calculated in ref.
17.
here (fig. 8) appear to be proportional to the projectile velocity at contact which agrees with the correlation seen in the inclusive measurements but at a factor of two less in absolute magnitude. A second system for which comprehensive information has been developed [19-211 is I60 +93Nb at 206
1
1
1
I
,
1
Fig. 8. As in fig. 7, except the non-equilibrium neutron source velocity is plotted. The straight line is a hot spot model fit (ref. 17) which gives a good account of the apparent slow source velocity.
Fig. 9. The differential a-particle multiplicity as a function of angle for ‘60+93Nb deep-inelastic reactions with a “C projectile fragment in coincidence. The arrow denotes the pre jectile fragment detection angles, about which the multiplicity is apparently asymmetric. Straightforward evaporation calculations give the dotted curve which disagrees with the observation. However, when the primary fragment angular distribution is correctly accounted for, the newly calculated multiplicity (solid line) is much better in agreement with the data (from ref. 19).
MeV (9 MeV per nucleon above the c.m. Coulomb barrier). In the deep-inelastic reactions, anisotropic forward peaked alpha-particle yields were observed (fig. 9). However, detailed calculations show that both the multiplicity and energies as a function of angle are consistent with emission from the fully accelerated fragments, provided that the rapid angular dependence of the primary projectile fragments’ differential cross sections is properly taken into account. Such is not the case for the neutron yields in deep-inelastic reactions of 160 +93Nb for which a significant number of forwardpeak, beam velocity particles were seen. This component could be fitted with a source velocity of 3.3 cm/ns and a low temperature of 1.5 MeV. These source parameters are not at all like those previously discussed which had a high temperature and a relatively low source velocity. The fusion-evaporation channel has also been measured for l6 0 + 93Nb at 206 MeV. One should realize that this system is practically identical wih the 160 + %Zr system discussed earlier on the basis of particle inclusive measurements. Singles measurements of 160 + 93Nb reveal the total reaction cross section to be 2600 mb, the fusion-evaporation cross section at 1050 mb, and the fusion-fission cross section at 300 mb. For comparison, the Bass fusion cross section [22] is 1500 mb, in good agreement with the experimental sum of fusion-evaporation and fusion-fission cross sections. These numbers are particularly relevant since a PACE Monte Carlo calculation [23] of the 160 +93Nb system gives an expected proton fusion-evaporation integrated III. NUCLEAR
PHYSICS/ASTROPHYSICS
C. F. Maguire / Non -equilibrium particle emission
446
I$
206
1_
MeV
I60
PROTON
+93Nb
RESIDUE-
f&=-13’
_T
20
25
ENERGY
30
35
40
45
50
(MEV)
Fig. 10. Proton multiplicity spectra measured in coincidence with fusion-evaporation residues for 206 MeV 160 + 93Nb. The residue angle is - 7.0°. The solid lines through the data points represent the moving source fits as normalized using the parameters given in fig. 1 for the very similar “O+ mZr system.
ENERGY
of 2.2, or about
2300 mb total cross section
of protons coming from simple evaporation alone. The moving source parameters of the nearly identical I60 +WZr system at 215 MeV (fig. 1) give an integrated yield of less than 1400 mb. Thus one must consider that a large fraction of the proton yield seen in fig. 1 is coming from evaporation, and this would compromise the extracted source parameters. The actuat fusion-evaporation yield of protons for l6 0 + 93Nb is shown in fig. 10, in terms of the differential multiplicity spectra for a fixed evaporation-residue detection angle and several proton detection angles. The energy spectra here are not cut off to exclude the compound nucleus maxima and low-energy roll-offs. Plotted in fig. 10 are the moving source fits based on the parameters of fig. 1. The fits at forward angles are excellent, unfortunately, but deteriorate at backward angles. The excellent forward angle fit is actually a severe blow to this model’s parameters since it means that the fusion evaporation component has been mistakenly included. This is specifically seen in fig. 11 which displays the PACE predicted multiplicity spectra. One sees good fits to the low energy yield at all angles, and the definite appearance of a non-equilibrium component at the most forward angles. If the evaporation
( MEV
1
Fig. 11. The same data as in fig. 10. The fits now are a combination of evaporation residue simulation, and a fa.rr, high temperature source whose contribution quickly fades with increasing observation angle. Id’
206
MeV
‘60 +=Nb
a -RESIDUE 9R’
multiplicity
4 MULTIPLICITY
t
MULTIPLICITY
130
-BREAK-VP
24
32
40
ENERGY
1
MODEL
48
56
I 64
I 72
80
(MEV)
Fig. 12. Alpha-particle multiplicity spectra for fusion-evaporation reactions of 206 MeV ‘60+93Nb. The fusion residue detection angle here is 13”. The dashed lines represent the complete fusion evaporation simulation from PACE. The solid lines represent the predictions of a break-up fusion process, described in the text.
C. F. Maguire / Non -equilibrium particle emission
simulation predictions are subtracted from the experimental multiplicity spectra, then a fit to the (remnant) non-equilibrium component, also shown in fig. 11, gives a high temperature and a high velocity source. The high velocity source is reminiscent of the deep-
447
inelastic neutron non-equilibrium results for this systern, but the high temperature fall-off is compatible with the 160 +90Zr inclusive study. With as high proton energies as seen in fig. 1, a very good temperature parameter can be extracted. The source velocity, how-
lo’
100
10-l
lo’
loo
IO'
2 %
s
Il.9
L
3
w” IO’ 4 “0 0
E
IO’
s loo
lo-’
loo
UT’
KT’
10-I
Ea UvleV) Fig. 13. Alpha particle spectra in coincidence with fusion-like residues for the reaction 316 MeV 160+@Ti (from ref. 24). There is clearly excess alpha emission at high energies, and apparently a group peaked at the beam velocity (80 MeV for the alpha particles.) III. NUCLEAR
PHYSICS/ASTROPHYSICS
C.F. Moguire / Non -equilibriumparticleemission
448
ever, depends critically on the compound nucleus contribution being correctly subtracted, which accounts for the great difference in proposed non-equilibrium source velocities in these two analyses. The non-equilibrium proton yield here (integrated multiplicity = 0.2 or 200 mb) is comparable to the deep-inelastic non-equilibrium neutron production but much lower than the 1400 mb concluded from the inclusive experiment. Compared to the “‘Yb compound nucleus non-equilibrium neutron results (figs 6-Q the 160 +93Nb fusion reaction noneqilibrium protons have much lower yield at the 9 MeV per nucleon velocity, the temperature is comparable, but the source velocity is much higher. If the high velocity is taken literally, than the non-equilibrium protons must be coming from the projectile prior to the fusion coalescence taking place. It is clear from these comparisons that different processes must be going on, and the adequacy of the second source parameterization to describe the non-equilibrium particle production universally must be questioned. The alpha particle evaporation yields for 160 + 93Nb at 206 MeV are also interesting. These are shown in fig. 12, along with the PACE predicted multiplicities. AS with the protons, the low energy component can be well understood as coming from simple evaporation. At for-
ward angles a second group is observed, whose yield is peaked at the beam velocity. As such it is likely that this second group can be understood as having a break-up fusion origin. Indeed, reasonably good fits to this second component can be obtained by modifying the PACE predicted multiplicities to include pre-excitation of the projectile above the alpha decay threshold and allowing for subsequent decay and detection of the alpha particle. By construction, the emitted alpha particle will possess a near-beam velocity energy. The remaining projectile fragment (“C) fuses with the target to provide the eventual evaporation residue. It is estimated that this process is relatively infrequent, and accounts for only 100 mb of the total evaporation residue yield. Excepting for the break-up fusion component, no non-equilibrium alpha-particle yield could be determined, which finding is in agreement with the deepinelastic alpha-particle analysis and contradicts the inclusive study’s conclusion for 160 + %Zr alpha-particle emission. The observation of alpha break-up fusion here is consistent with the data 1241 on 160 +&Ti at 316 MeV, shown in fig. 13. The beam velocity alpha group is
1’“‘I”“I”. _ “Si *‘*C * _ 254 +%q .
1.05-
*ssi l*‘si 0 msi +4oca l
I ‘60+‘2c . ‘So+ %4g ‘60 + *‘si
o
‘60+40~
.
I,,
1.0 Jw 0
40
80
I20
160 200
EFLR (MeV)
Fig. 14. Energy spectra of the fusion-like residues for the reaction given in fig. 13. The dotted, dashed and continuous lines give the simulation alpha-particle break-ups (from ref. 24).
predictions for one, two, and three contributing to a fusion-like event
I
I;
. . I . . . . I,. 3.0
2.0 (Me’?)
Fig. 15. Part (a) gives the ratio of the measured fusion-residue centroid velocitks compared to the complete fusion-expected velocities for several different reaction combinations at increasing energies above the Coulomb barrier. Part b) gives the apparent number of non-equilibrium nucleons for a subset of the reactions shown in a) (from refs. 25-28). The curves in part (b) are Fermi sphere overlap calculations described in ref. 25.
C. F. Maguire
252Mev
=s1
l
PROTON-RESIDUE
4%
/
Non -equilibrium
MULTlPLtClTY
ENERGY
t&=-6.5O
(MEV)
4. Resolved fusion-evaporation coincidence data
prominent here, and by including various alpha break-up channels, one is able to fit the singles residue spectral shapes in these fusion reactions at various observation angles (see fig. 14).
aaSi + 4oCo
I
Id’C)
4
I
8
I
12
PROTON-RESIDUE
I
16
I
The previous examples of non-equilibrium particle central collision coincidence experiments have summed
MULTIPLICITY
I
20
1
Fig. 16. Proton multiplicity spectra measured for fusion-evaporation reactions of 252 MeV 2sSi+40Ca. The solid lines through the data points represent the predictions of the complete fusion evaporation program PACE. There is little, if any, evidence of non-equilibrium particle production at high energies even at these forward angles.
dramatically
(252MeV
449
particle emission
24
ENERGY
e,=-6.5”
I
I
I
I
28
32
36
40
( MEV 1
I
44
I
48
52
Fig. 17. As in fig. 16, except for more backward proton detection angles. Apparently all the yield is coming from fusion-evaporation.
III. NUCLEAR PHySICS/ASPROPHySICS
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C. F. Maguire / Non - equilibrium particle emission
252MeV
2%
+ 40Ca
a-RESIDUE
MULTIPLICITY
8 =-6.5’
Fig. 18. As in fig. 16 except that alpha-particle multiplicity is presented. Only the highest energy region of the two forward opposite side detectors shows deviations from the PACE predicted multiplicity. The non-equilibrium yield is apparently minimal. At low energies the calculation overpredicts the observed yields, indicating refinement is needed in the Coulomb barrier approximation.
-26”
I8 16’0
(2,
r
t
I
8
I
16
I
24
I
I
32
I 40
I 40
I 56
I 64
\ 72
over the coincidence gate, be it fusion-fission fragments, or fusion-evaporation residues. More precise, although obviously less extensive, information can be gleaned by resolving the gated heavy particle as to its
MeV
%ji
+40Ca
a-RESIDUE
I 88
( MEV)
ENERGY
252
I
00
MULTIPLICITY
velocity and mass. This type of experiment is just now being undertaken and extends the previous singles residue velocity measurements whose results [25-281 are summarized in fig. 15. This is a plot of the centroid
8,=-6J”
I
3
r
Id90
,
.I8
16I
24I
32I
, ,lCXl”, 40 48 ENERGY
I
5 86
( MEV 1
I 64
I
72
I
80
I 88
I 96
Fig. 19. As in fig. 18 for the more backward alpha-particle detection angles. The overprediction of the low-energy alpha yield is very apparent here.
451
C. F. Maguire / Non -equilibrium particle emission
16o~eV
‘60 + ‘%a
PROTON-RESIDUE
MULTIPLICITY
6,=-g”
I
Fig. 20. The proton multiplicity spectra for the fusion-evaporation reactions of 160 MeV 160+%a. The curves are again PACE-predicted multiplicities for complete fusion evaporation. Unlike the %i proton multiplicity spectra, the high-energy regions here display definite higher temperature components at forward angles. These yields are much less, though, than the 160 + 93Nb non-equilibrium proton yields coming at a higher projectile velocity (fig. 11).
ENERGY (ME’.‘)
from full momentum transfer begin to set in at projectile energies several MeV per nucleon above the Coulomb barrier. However, no firm conclusion can be drawn from these singles results as to the origin of
velocities of the residue fragments as a function of projectile velocity for many different’ projectile-target combinations. Similar to the threshold which has been seen in the non-equilibrium particle studies, deviations
160 MeV
‘60
+ WC0
a-RESIDUE
MULTIPLICITY
f&-9’
t-r,_
r
l6”O
I
I
I
8
I6
24
32
40
48
56
ENERGY (MEV)
64
72
80
,
88
-65~
IO4
Fig. 21. As in fig. 20, except the alpha-particle multiplicity spectra are plotted. There is again evidence of non-equilibrium particle production at forward angles, especially at the 25” position. This spectrum appears to have a beam velocity group (40 MeV) similar to that seen in the 316 MeV 160+Ti data shown in fig. 13.
III. NUCLEAR PHYSICS/ASTROPHYSICS
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C. F. Maguire
/ Non -equilibrium particle emission
momentum deficit. Quite clearly the break-up fusion process described at the end of the last section will result in incomplete momentum transfer but break-up fusion is not as interesting as hot spot production, for example. Two experiments have been done recently that wmbine the techniques of energetic light-particle measurement and resolved heavy-particle velocity spectroscopy. The systems measured were 252 MeV ?ji on &Ca (6 MeV per nucleon above the Coulomb barrier) and 160 MeV 160 on @Ca (7 MeV per nut 1w n above the barrier). For the ‘*Si induced reactions, a 1.1 m timeof-flight (TOF) telescoped analyzed the fusion-evaporation residues, obtaining better than unit mass resolution up to about mass 63, the highest mass remaining from the A = 68 compound nucleus. The centroid velocity for the inclusive residue particles was consistent with no velocity shift coming from less than full momentum transfer. The coincident light-particle multiplicity spectra (figs. 16-19) bear this fact out. Both the proton and the alpha particle multiplicity shapes and magnitudes are very well reproduced by the PACE calculations. No non-equilibrium high-energy particles are discernible, not even an alpha-particle break-up fusion group at beam velocity. What is interesting about this null result is that at the 6 MeV per nucleon above the Coulomb barrier characterizing this system, a substantial nonequilibrium production was evident for the “‘Yb nonequilibrium neutron production (fig. 6) in fusionevaporation residue coincidence. The second system measured, 160 +40Ca, exhibited a 7% momentum deficit for the inclusive residue centroid velocity value. This deficit can be correlated with the existence of non-equilibrium particle production as seen in figs. 20-21, illustrating the proton- and the alphaparticle multiplicity spectra. The PACE predicted spectra are generally able to reproduce the maxmima of these spectra, but towards high energy at forward angles there is too much experimental yield. For the protons, there is apparently a small high-temperature wmponent, with much less strength than the non-equilibrium yield seen in the t60 +93Nb reactions. For the alpha particles, there is also apparently a beam velocity wmponent especially at the 25O light particle observation angle. Again, given the high velocity above the Coulomb barrier, the non-equilibrium yield for this reaction does not compare with the systematics seen in the “‘Yb production. Granted the low velocity source seen in that experiment, it is possible that the neutrons derived from forward recoiling target nuclei before full momentum transfer took place. For the lighter nuclei considered here, the neutron excess is not as pronounced and the multiplicities are reduced. One wmes once more to the conclusion that in non-equilibrium production several different processes are responsible.
5. Summary and conclusions
Non-equilibrium particle production has been studied in coincidence with fusion-evaporation residue detection, corresponding to near full momentum, central collisions taking place. These data, when analyzed in terms of moving source model parameters, yield very different values for the temperature and the source velocities. In some, cases, such as non-equilibrium experiments on heavy targets, the source appears to be the target system prior to fusion. For 160 +93Nb at 206 MeV, the source seems to be the projectile, again prior to fusion. There is also a great difference in the magnitude of the non-equilibrium particle production, again the heavy-target neutron experiments being more prolific. At comparable energies above the Coulomb barrier, experiments on 40Ca have shown only small or no non-equilibrium production. It is clear that one has now reached the point where the microscopic nucleon-nucleon interactions will have to be addressed in order to understand these variations in non-equilibrium particle production. It is a pleasure to acknowledge the contributions of Drs Glenn Young, Terry Awes and F. Plasil of Oak Ridge National Laboratory, and Drs Dermis Kovar, Gunther Rosner and Hiroshi Ikezoe of Argonne National Laboratory for their contributions to this study. Research at Vanderbilt University is supported in part by U.S.D.O.E. grant No. DE-ASO576ER05034.
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M.L. Halbert, P.O. Tjom, I. Espe, G.H. Hagemann, B. Herskind, M. Nieman and H. Oesehler, Nucl. Phys. A259
(1976) 496. [3] L. Westerberg, D.G. Sarantites, D.C. Hensley, R.A. Dayras and J.H. Barker, Phys. Rev. Cl8 (178) 976. [4] Y. Eyal, A. Gavron, I. Tserruya, Z. Fraenkel, Y. Eisen, S. Wald, R. Bass, G.R. Gould, G. Kreyling, R. Renfordt, K. Stelzer, I. Rode and R. Bock, Phys. Rev. Lett 41 (1978) 625. [5] D. Hihcher, J.R. Birkelund, A.D. Hoover, W.U. Schroeder, W.W. Wilcke, J. Huizinga, A.C. Mignerey, K.L. Wolf, H. Breuer and V.E. Viola Jr, Phys. Rev. C20 (1979) 576. [6] M. Bini, C.K. Gelbke, D.K. Scott, T.J.M. Symons, P. Doll, D.L. Hendrie, J.L. Laville, J. Mahoney, M.C. Mermaz, C. Ohner, K. Van Bibber and H.H. Wieman, Phys. Rev. C22 (1980) 1945. [7] R.L. Robinson, R.L. Auble, J.B. Ball, F.E. Bertrand, R.L. Ferguson, C.B. Fulmer, J. Gomez de1 CamPo, I.Y. Lee, R.W. Novotny, G.R. Young, J.C. Wells, CF. Maguire and H. Yamada, Phys. Rev. C27 (1983) 3006. [8] T. Fukuda, M. Ishihara, M. Tanaka, H. Ogata, I. Miura,
C.F. Maguire / Non -equilibrium particle emission M. Inoue, T. Shimoda, K. Katoti and S. Nakayama, Phys. Rev. C27 (1983) 2029. [9] I. Tserruya, A. Breskin, Z. Fraenkel, S. WaId, R. Bock, M. Dakowski, A. Gobbi, H. Sann, R. Bass, G. Kreyling, R. Renfordt, K. SteIzer and U. Arit, Phys. Rev. Lett. 47 (1981) 16. [lo] A. Gavron, J.R. Beene, R.L. Ferguson, F.E. Obenshain, F. PlasiI, G.R. Young, G.A. Petitt, K. Geoffroy-Young, M. Jaaskelainen, D.G. Sarantites and CF. Maguire, Phys. Rev. C24 (1981) 2048. [ll] R. Weiner and M. Westrom, Nucl. Phys. A286 (1977) 282. [12] P.A. GottschaIk and M. Westrom, Nucl. Phys. A314 (1979) 232. [13] T.C. Awes, G. Poggi, S. Saini, C.K. Gelbke, D. Cha, R. Legrain and G.D. WestfaIl, Phys. Rev. C25 (1982) 2361. [14] B.B. Back, K.L. Wolf, A.C. Mignerey, C.K. Gelbke, T.C. Awes, H. Breuer, V.E. Viola Jr. and P. Dyer, Phys. Rev. C22 (1980) 1927. [15] J. Kasagi, S. Saini, T.C. Awes, A. Galonsky, C. Gelbke, G. Poggi, D.K. Scott, K.L. Wolff and R. Legrain, Phys. Lett. 104B (1981) 434. [16] T.C. Awes, G. Poggi, C.K. Gelbke, B.B. Back, G.G. Glagola, H. Breuer and V.E. Viola Jr. Phys. Rev. C24 (1981) 89. 1171A. Gavron, J.R. Beene, B. Cheynis, R.L. Ferguson, F.E. Obenshain, F. PlasiI, G.R. Young, G.A. Petit& C.F. Maguire, D.G. Sarantites, M. Jaaskelainen and K. GeoffroyYoung, Phys. Rev. C27 (1983) 450. [18] M. Blann, Phys. Rev. C23 (1981) 205.
453
[19] G.R. Young, R.L. Ferguson, A. Gavron, D.C. Hensley, F.E. Obenshain, F. P&l, A.H. SneII, M.P. Webb, C.F. Maguire and G.A. Petitt, Phys. Rev. Lett. 17 (1980) 1389. 1201 A. Gavron, R.L. Ferguson, F.E. Obenshain, F. Plasil, G.R. Young, G.A. Petitt, K. Geoffroy-Young, D.G. Sarantites and C.F. Maguire, Phys. Rev. Lett. 46 (1981) 8. [21] C.F. Maguire, B. Cheynis, R.L. Ferguson, I-Y Lee, R. Novotony, F.E. Obenshain, D. Pelte, F. Plasil, R.L. Robinson and G.R. Young, BuII. Am. Phys. Sot. 28 (1983) 717. [22] R.Bass, Phys. Rev. L&t. 39 (1977) 265. [23] M. Hillman and Y. EyaI, unpublished; A. Gavron, Phys. Rev. C21 (1980) 230. [24] P. Gonthier, H. Ho, M.N. Namboodiri, J.B. Natowitz, L. Alder, S. Kniffen and A. Khodai, Nucl. Phys. A411 (1983) 289. [25] G.S.F. Stehphans, D.G. Kovar, R.V.F. Jansens, G. Rosner, H. Ikezoe, B. Wilkins, D. Henderson, K.T. Lesko, J.J. Kolata, C. Gelbke, B. Jacak, Z. Koenig, G. WestfaII, A. Szanto de Toledo, E.M. Szanto and P. Gonthier, preprint (1984). [26] R. BiIIerey, C. Cerruti, A. Chevarier, N. Chevarier, G. Cheynis, A. Demeyer and M.N. Namboodiri, Phys. Rev. Lett. 47 (1981) 639. (271 H. Morgenstem, W. Bohne, K. Grab&h, D.G. Kovar and H. Lehr, Phys. Lett. 113B (1982) 463. [28] Y. Ghan, M. Murphy, R.G. Stokstad, I. Tserruya, S. Wald and A. Budzanowski, Phys. Rev. C27 (1983) 447.
III. NUCLEAR PHYSICS/ASTROPHYSICS
NON-~~~~ REACIIONS Charles Department
441
(1985) 441-453
PARTICLE EMISSION IN HEAVY-ION ~SION-EVANSTON
F. MAGUIRE of
Physics and Astronomy, Vanderbiiit University, Nashvilie, TN 37.235, USA
Non-equilibrium particle emission occurxing in heavy-ion fusion-evaporation reactions is analyzed in terms of the moving source model. Different projectile-target combinations are. seen to give different source characteristics depending upon the particle being detected. Non-equilibrium particle production in a heavy projectile reaction, **Si+ *Ca, is practically non-existent even at a relatively high projectile v&city aboye the koulomb barrier.
1. inbwhrction
For projectile energies having only a few MeV per nucleon above the Coulomb barrier in nucleus-nucleus collisions, the light-particle (neutron, proton, alpha) emission spectra appear to be well understood in terms of the statistical decay of temperature equilibrated systems. This is true for complete fusion compound nucleus formation [l-3] as well as for deep-inelastic collisions [4-61. At a certain threshold, perhaps 5 MeV per nucleon above the barrier, non-equilibrium components have been identified in the particle emission spectra for a wide variety of experiments [7-lo]. It is tempting to think of the origin of these energetic particles in thermodynamic concepts. That is the thermal conductivity limit of nuclear matter has been breached and too much kinetic energy has to be dissipated too fast at the collision boundary. More specifically, a hot spot [xl-121 of nuclear matter develops, consisting of a restricted subset of the colliding nucieons and responsible for non-equilibrium particle production. On the other hand, these non-equilibrium features may reflect new facets of the nucl~s-nucleus collision as the mean-field induced phenomena receive competition from nucleon-nucleon interactions at the higher projectile velocities with reduced Pauli blocking. In any event the study of the emission of energetic light particles will illuminate the dynamics of the heavy-ion reaction process at its earliest stages. The subject of this paper will focus on energetic particle emission in fusion-evaporation reactions which will complement the results already in hand from fusion-fission reactions and deep-inelastic studies. 2. shtgles aystematiea A seminal earlier inclusive experiment [13] measured the proton, deuteron, Won, and alpha particle spectra 016%583X/85/$03.30 0 Blsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
produced in 160 induced reactions at 5 to 16 MeV per nucleon above the barrier on targets of mass A = 27 to A = 197. A typical result is depicted in fig 1, which shows the proton singles spectra at 215 and 310 MeV for the target “Zr. These spectr a display exponentially decreasing structureless tails going out to 3 or 4 times @teincident beam velocity of 13 or 19 MeV per nucleon. The slopes change with angle, becoming steeper at more backward angles suggesting some source motion is required. In this experiment a low energy cut-off of 12 MeV (Z=l), or 30 MeV (Z-2), was in place so the compound nucleus evaporation peak and roll-off at low energy are not visible. The spectra can be fitted in general by a moving Maxwellian source, characterized by its own temperature T and a velocity u paraBe to the beam velocity. Transforming to the lab and including Coulomb repulsion from the target, one obtains the double differential cross section as:
where EC = Coulomb repulsion energy after emission, E, = source “velocity” (MeV/amu), 8 = lab detection angle, T = source temperature, N, = source strength, energy and angle integrated yield: CJ= 2No(prT)‘/‘. The temperature T and the source velocity u parameters are extracted according to the fits of this function to the data. The smooth trends of these parameters are illustrated in fig. 2 from this experiment. One sees for the two heavier targets measured that both the temperature and the source velocity appear to track linearly with the projectile velocity above the barrier, and both parameters disagree with the values expected from just compound nucleus production alone. In particuhu, the source velocity is about half the beam velocity, indicating in this analysis that only a partial fraction of the III. NUCLEAR PHYSICS/ASTROPHYSICS
C.F. Maguire / Non -equilibrium particle emission
442
160+9OZr+p+X
l
EXPERIMENT
- MOVING
SOURCE
10’3 10’2
310 _
I_
-
T
=
9.B
Er
=
5.0
=
5.73
MeV MeV MeV
MeV
Fig. 1. Inclusive proton spectra of I60 on 90Zr for projectile energies of 215 and 310 MeV (from ref. 13).
The curves through the data points 80
ENERGY
total
[MeV)
nucleus is interacting to produce the energetic light particles. Of course, one should not push the inclusive measurements too hard since there can clearly be many effects contributing to the measured particle spectra. Detailed questions as to the origin of the energetic particles can only be answered by coincidence studies. An innovative technique in this regard was the study [14] of particle correlations in fusion-fission reactions. The fission fragments are detected in coincidence and their opening angle determines the degree of linear momentum transferred in the collision (fig. 3). Opening angles near 180” signify peripheral type collisions while smaller opening angles reflect central collisions corresponding to near complete fusion of the projectile and the target. Fig. 4 shows the results [15] of neutron spectra in coincidence with (single) fission fragments for 160 on 238U at 310 MeV. Two components in the spectra are seen, coming from compound nucleus evaporation of fission fragment decay, and from neuiron emission before equilibration has occurred. The origin of the light particles is seen in the proton emis-
160 are moving source model predictions as described in the text.
sion channel, shown in fig. 5, where one now also has information on the opening angle of the fission fragments [16]. One infers conclusively from these coincidence data that the intermediate angle yields come almost completely from the full momentum transfer, central collisions, equivalently the compound nucleus. On lighter mass targets, for which the compound nucleus fission barriers are much higher, similar information can be obtained by gating on the fusion-evaporation residues whose velocities and mass give an unambiguous signal of large momentum transfer.
3. Summed fusion-evaporation
coincidence data
A systematic measurement [17] of non-equilibrium neutron emission has been made for “(2, 13C, and *ONe projectiles at specific energies on selected targets, all leading to the same compound nucleus, “‘Yb, at comparable excitation energies. Neutron spectra were collected in coincidence with fusion-evaporation residues detected at a forward angle. As was the case for the
C. F. Maguire / Non -equilibrium pariicle emission
8.
6-
160+23*u
MOVING SOURCE PARAMETERS INCLUSIVE PROTONS
310
l-
+
n+f
1
MeV
0.
0) 10‘
z E
443
4-
10’ 7 ‘z u-l ;
‘O’
f 10‘
.a-
b) c:
10’
.06 % z’
10’
\. C-F -0
10’
10’
lo-
Fig. 2. Systematics of the moving source model parameters derived in ref. 13. According to this analysis, the source of the high energy protons was not the compound nucleus, but a higher temperature region moving at near the nucleon-nucleon collision velocity.
10’
ENERGY
[MeV)
Fig. 4. Neutron spectra in coincidence with fission fragments for the reaction of 1sO+23sU at 310 MeV. Note the two components, low and high temperature, detection angles (from ref. 15).
visible at all neutron
neutrons shown in fig. 3, the evaporation residue gated neutrons here displayed two components, one with a low temperature obviously coming from the compound nucleus, and the second of a much higher temperature and concentrated in yield at forward angles. The results of this study are summarized in figs. 6-8, in terms of the non-equilibrium neutron multiplicity, and the temperature and velocity of the apparent source of these
Fig. 3. Plot of the opening angIe between coincident fission fragments, showing the division between peripheral collisions (small linear momentum transfer, larger opening angles) and central collisions (near full momentum transfer, smaller opening angles). The deep-inelastic projectile-like fragments are seen to be associated with the peripheral collisions, as expected, (from ref. 14).
III. NUCLEAR PHYSICS/ASTROPHYSICS
444
C. F. Maguire
/
Non -equilibrium
parricle emission
I ‘sO+238U-X
4
:
.
:::::t:::::: x=t
Et>15
lo-2
lO-3 7
l
.
0 Sum A 0 Cantrol A Peripheral
O.lr
:
1
0 0
.
c : 10-4 r
MeV
.
clo-5-::::::t+:::; 0
-0
A
.
10-3
T
rn’@
8
.
TL v,
315
0
.
lo-2/
f,
b A
.
4 .a
a @ . .
‘:
8
. ‘@ *
0 A 8 ‘5
10-4r
. . .,,.,,.,,.,,,. 30 60
90
-!
. .,,,.I,.,,,,., 120 0 30 60 8, K!EGREES)
. 90
120
Fig. 5. Charged light particle spectra measured in coincidence with fission fragments for the reaction ‘60+23sU more backward angle yields are. seen to be almost exclusively associated with central collisions (from ref. 16).
at 315 MeV. The
energetic
mzutrons. When plotted as a function of the projectile energy per nucleon above the barrier, the non-equilibrium multiplicity appears to increase linearly, and independently of the projectile being considered. The velocity trend is in line with the predictions of the Boltzmann Master Equation model [18] (BME) but that model predicts, incorrectly, very different multiplicities as a function of projectile mass. The temperature of the non-equilibrium neutrons (fig. 7) appears nor to depend strongly on the projectile velocity in contradiction to the inclusive charged particle measurements discussed above [13] and also in marked contrast to the predictions of the BME model. The pattern of constant temperature values also is inconsistent with the increasing temperature values predicted by a derivation [17] based on the hot-spot picture. The source velocities
01 0
’
’
4
’
’
4
’
( EC,,,-Vc I/&
’s
’
’ e
’
’ ’ IO
N'eV~nuc~eon)
I2
Fig. 6. Non-equilibrium neutron multiplicity for 12C, 13C, and “Ne induced fusion-evaporation reactions all leading to 170Yb. The non-equilibrium multiplicities are plotted as function of the c.m. energy above the Coulomb barrier per nucleon. The open circles are 12C, the full circles are “C, and the triangles mNe data points. The straight lines A, B and C represent BME fits (see text) for 12C, 13C and 20Ne, respectively (from rcf 17).
C. F. Maguire
/
Non -equilibrium
445
particle emission
204
MeV ‘%+=Nb
c-a
e,, =-21’
5m
e-
._
2-
-80
0
80
8, (lab1 MegI
01 0
’
’
’
2
’
’
’
’
’
’
’
Y)
4 6 0 (E c,_.‘vc ) /#a(MeVhluckan~
1
’
t2
Fig. 7. As in fig. 6, expect the non-equilibrium neutron source temperature is plotted. The solid lines are the BME model predictions, the dashed line is the result m-portedin ref. 13, and the dashed-dotted line is a hot-spot model fit calculated in ref.
17.
here (fig. 8) appear to be proportional to the projectile velocity at contact which agrees with the correlation seen in the inclusive measurements but at a factor of two less in absolute magnitude. A second system for which comprehensive information has been developed [19-211 is I60 +93Nb at 206
1
1
1
I
,
1
Fig. 8. As in fig. 7, except the non-equilibrium neutron source velocity is plotted. The straight line is a hot spot model fit (ref. 17) which gives a good account of the apparent slow source velocity.
Fig. 9. The differential a-particle multiplicity as a function of angle for ‘60+93Nb deep-inelastic reactions with a “C projectile fragment in coincidence. The arrow denotes the pre jectile fragment detection angles, about which the multiplicity is apparently asymmetric. Straightforward evaporation calculations give the dotted curve which disagrees with the observation. However, when the primary fragment angular distribution is correctly accounted for, the newly calculated multiplicity (solid line) is much better in agreement with the data (from ref. 19).
MeV (9 MeV per nucleon above the c.m. Coulomb barrier). In the deep-inelastic reactions, anisotropic forward peaked alpha-particle yields were observed (fig. 9). However, detailed calculations show that both the multiplicity and energies as a function of angle are consistent with emission from the fully accelerated fragments, provided that the rapid angular dependence of the primary projectile fragments’ differential cross sections is properly taken into account. Such is not the case for the neutron yields in deep-inelastic reactions of 160 +93Nb for which a significant number of forwardpeak, beam velocity particles were seen. This component could be fitted with a source velocity of 3.3 cm/ns and a low temperature of 1.5 MeV. These source parameters are not at all like those previously discussed which had a high temperature and a relatively low source velocity. The fusion-evaporation channel has also been measured for l6 0 + 93Nb at 206 MeV. One should realize that this system is practically identical wih the 160 + %Zr system discussed earlier on the basis of particle inclusive measurements. Singles measurements of 160 + 93Nb reveal the total reaction cross section to be 2600 mb, the fusion-evaporation cross section at 1050 mb, and the fusion-fission cross section at 300 mb. For comparison, the Bass fusion cross section [22] is 1500 mb, in good agreement with the experimental sum of fusion-evaporation and fusion-fission cross sections. These numbers are particularly relevant since a PACE Monte Carlo calculation [23] of the 160 +93Nb system gives an expected proton fusion-evaporation integrated III. NUCLEAR
PHYSICS/ASTROPHYSICS
C. F. Maguire / Non -equilibrium particle emission
446
I$
206
1_
MeV
I60
PROTON
+93Nb
RESIDUE-
f&=-13’
_T
20
25
ENERGY
30
35
40
45
50
(MEV)
Fig. 10. Proton multiplicity spectra measured in coincidence with fusion-evaporation residues for 206 MeV 160 + 93Nb. The residue angle is - 7.0°. The solid lines through the data points represent the moving source fits as normalized using the parameters given in fig. 1 for the very similar “O+ mZr system.
ENERGY
of 2.2, or about
2300 mb total cross section
of protons coming from simple evaporation alone. The moving source parameters of the nearly identical I60 +WZr system at 215 MeV (fig. 1) give an integrated yield of less than 1400 mb. Thus one must consider that a large fraction of the proton yield seen in fig. 1 is coming from evaporation, and this would compromise the extracted source parameters. The actuat fusion-evaporation yield of protons for l6 0 + 93Nb is shown in fig. 10, in terms of the differential multiplicity spectra for a fixed evaporation-residue detection angle and several proton detection angles. The energy spectra here are not cut off to exclude the compound nucleus maxima and low-energy roll-offs. Plotted in fig. 10 are the moving source fits based on the parameters of fig. 1. The fits at forward angles are excellent, unfortunately, but deteriorate at backward angles. The excellent forward angle fit is actually a severe blow to this model’s parameters since it means that the fusion evaporation component has been mistakenly included. This is specifically seen in fig. 11 which displays the PACE predicted multiplicity spectra. One sees good fits to the low energy yield at all angles, and the definite appearance of a non-equilibrium component at the most forward angles. If the evaporation
( MEV
1
Fig. 11. The same data as in fig. 10. The fits now are a combination of evaporation residue simulation, and a fa.rr, high temperature source whose contribution quickly fades with increasing observation angle. Id’
206
MeV
‘60 +=Nb
a -RESIDUE 9R’
multiplicity
4 MULTIPLICITY
t
MULTIPLICITY
130
-BREAK-VP
24
32
40
ENERGY
1
MODEL
48
56
I 64
I 72
80
(MEV)
Fig. 12. Alpha-particle multiplicity spectra for fusion-evaporation reactions of 206 MeV ‘60+93Nb. The fusion residue detection angle here is 13”. The dashed lines represent the complete fusion evaporation simulation from PACE. The solid lines represent the predictions of a break-up fusion process, described in the text.
C. F. Maguire / Non -equilibrium particle emission
simulation predictions are subtracted from the experimental multiplicity spectra, then a fit to the (remnant) non-equilibrium component, also shown in fig. 11, gives a high temperature and a high velocity source. The high velocity source is reminiscent of the deep-
447
inelastic neutron non-equilibrium results for this systern, but the high temperature fall-off is compatible with the 160 +90Zr inclusive study. With as high proton energies as seen in fig. 1, a very good temperature parameter can be extracted. The source velocity, how-
lo’
100
10-l
lo’
loo
IO'
2 %
s
Il.9
L
3
w” IO’ 4 “0 0
E
IO’
s loo
lo-’
loo
UT’
KT’
10-I
Ea UvleV) Fig. 13. Alpha particle spectra in coincidence with fusion-like residues for the reaction 316 MeV 160+@Ti (from ref. 24). There is clearly excess alpha emission at high energies, and apparently a group peaked at the beam velocity (80 MeV for the alpha particles.) III. NUCLEAR
PHYSICS/ASTROPHYSICS
C.F. Moguire / Non -equilibriumparticleemission
448
ever, depends critically on the compound nucleus contribution being correctly subtracted, which accounts for the great difference in proposed non-equilibrium source velocities in these two analyses. The non-equilibrium proton yield here (integrated multiplicity = 0.2 or 200 mb) is comparable to the deep-inelastic non-equilibrium neutron production but much lower than the 1400 mb concluded from the inclusive experiment. Compared to the “‘Yb compound nucleus non-equilibrium neutron results (figs 6-Q the 160 +93Nb fusion reaction noneqilibrium protons have much lower yield at the 9 MeV per nucleon velocity, the temperature is comparable, but the source velocity is much higher. If the high velocity is taken literally, than the non-equilibrium protons must be coming from the projectile prior to the fusion coalescence taking place. It is clear from these comparisons that different processes must be going on, and the adequacy of the second source parameterization to describe the non-equilibrium particle production universally must be questioned. The alpha particle evaporation yields for 160 + 93Nb at 206 MeV are also interesting. These are shown in fig. 12, along with the PACE predicted multiplicities. AS with the protons, the low energy component can be well understood as coming from simple evaporation. At for-
ward angles a second group is observed, whose yield is peaked at the beam velocity. As such it is likely that this second group can be understood as having a break-up fusion origin. Indeed, reasonably good fits to this second component can be obtained by modifying the PACE predicted multiplicities to include pre-excitation of the projectile above the alpha decay threshold and allowing for subsequent decay and detection of the alpha particle. By construction, the emitted alpha particle will possess a near-beam velocity energy. The remaining projectile fragment (“C) fuses with the target to provide the eventual evaporation residue. It is estimated that this process is relatively infrequent, and accounts for only 100 mb of the total evaporation residue yield. Excepting for the break-up fusion component, no non-equilibrium alpha-particle yield could be determined, which finding is in agreement with the deepinelastic alpha-particle analysis and contradicts the inclusive study’s conclusion for 160 + %Zr alpha-particle emission. The observation of alpha break-up fusion here is consistent with the data 1241 on 160 +&Ti at 316 MeV, shown in fig. 13. The beam velocity alpha group is
1’“‘I”“I”. _ “Si *‘*C * _ 254 +%q .
1.05-
*ssi l*‘si 0 msi +4oca l
I ‘60+‘2c . ‘So+ %4g ‘60 + *‘si
o
‘60+40~
.
I,,
1.0 Jw 0
40
80
I20
160 200
EFLR (MeV)
Fig. 14. Energy spectra of the fusion-like residues for the reaction given in fig. 13. The dotted, dashed and continuous lines give the simulation alpha-particle break-ups (from ref. 24).
predictions for one, two, and three contributing to a fusion-like event
I
I;
. . I . . . . I,. 3.0
2.0 (Me’?)
Fig. 15. Part (a) gives the ratio of the measured fusion-residue centroid velocitks compared to the complete fusion-expected velocities for several different reaction combinations at increasing energies above the Coulomb barrier. Part b) gives the apparent number of non-equilibrium nucleons for a subset of the reactions shown in a) (from refs. 25-28). The curves in part (b) are Fermi sphere overlap calculations described in ref. 25.
C. F. Maguire
252Mev
=s1
l
PROTON-RESIDUE
4%
/
Non -equilibrium
MULTlPLtClTY
ENERGY
t&=-6.5O
(MEV)
4. Resolved fusion-evaporation coincidence data
prominent here, and by including various alpha break-up channels, one is able to fit the singles residue spectral shapes in these fusion reactions at various observation angles (see fig. 14).
aaSi + 4oCo
I
Id’C)
4
I
8
I
12
PROTON-RESIDUE
I
16
I
The previous examples of non-equilibrium particle central collision coincidence experiments have summed
MULTIPLICITY
I
20
1
Fig. 16. Proton multiplicity spectra measured for fusion-evaporation reactions of 252 MeV 2sSi+40Ca. The solid lines through the data points represent the predictions of the complete fusion evaporation program PACE. There is little, if any, evidence of non-equilibrium particle production at high energies even at these forward angles.
dramatically
(252MeV
449
particle emission
24
ENERGY
e,=-6.5”
I
I
I
I
28
32
36
40
( MEV 1
I
44
I
48
52
Fig. 17. As in fig. 16, except for more backward proton detection angles. Apparently all the yield is coming from fusion-evaporation.
III. NUCLEAR PHySICS/ASPROPHySICS
450
C. F. Maguire / Non - equilibrium particle emission
252MeV
2%
+ 40Ca
a-RESIDUE
MULTIPLICITY
8 =-6.5’
Fig. 18. As in fig. 16 except that alpha-particle multiplicity is presented. Only the highest energy region of the two forward opposite side detectors shows deviations from the PACE predicted multiplicity. The non-equilibrium yield is apparently minimal. At low energies the calculation overpredicts the observed yields, indicating refinement is needed in the Coulomb barrier approximation.
-26”
I8 16’0
(2,
r
t
I
8
I
16
I
24
I
I
32
I 40
I 40
I 56
I 64
\ 72
over the coincidence gate, be it fusion-fission fragments, or fusion-evaporation residues. More precise, although obviously less extensive, information can be gleaned by resolving the gated heavy particle as to its
MeV
%ji
+40Ca
a-RESIDUE
I 88
( MEV)
ENERGY
252
I
00
MULTIPLICITY
velocity and mass. This type of experiment is just now being undertaken and extends the previous singles residue velocity measurements whose results [25-281 are summarized in fig. 15. This is a plot of the centroid
8,=-6J”
I
3
r
Id90
,
.I8
16I
24I
32I
, ,lCXl”, 40 48 ENERGY
I
5 86
( MEV 1
I 64
I
72
I
80
I 88
I 96
Fig. 19. As in fig. 18 for the more backward alpha-particle detection angles. The overprediction of the low-energy alpha yield is very apparent here.
451
C. F. Maguire / Non -equilibrium particle emission
16o~eV
‘60 + ‘%a
PROTON-RESIDUE
MULTIPLICITY
6,=-g”
I
Fig. 20. The proton multiplicity spectra for the fusion-evaporation reactions of 160 MeV 160+%a. The curves are again PACE-predicted multiplicities for complete fusion evaporation. Unlike the %i proton multiplicity spectra, the high-energy regions here display definite higher temperature components at forward angles. These yields are much less, though, than the 160 + 93Nb non-equilibrium proton yields coming at a higher projectile velocity (fig. 11).
ENERGY (ME’.‘)
from full momentum transfer begin to set in at projectile energies several MeV per nucleon above the Coulomb barrier. However, no firm conclusion can be drawn from these singles results as to the origin of
velocities of the residue fragments as a function of projectile velocity for many different’ projectile-target combinations. Similar to the threshold which has been seen in the non-equilibrium particle studies, deviations
160 MeV
‘60
+ WC0
a-RESIDUE
MULTIPLICITY
f&-9’
t-r,_
r
l6”O
I
I
I
8
I6
24
32
40
48
56
ENERGY (MEV)
64
72
80
,
88
-65~
IO4
Fig. 21. As in fig. 20, except the alpha-particle multiplicity spectra are plotted. There is again evidence of non-equilibrium particle production at forward angles, especially at the 25” position. This spectrum appears to have a beam velocity group (40 MeV) similar to that seen in the 316 MeV 160+Ti data shown in fig. 13.
III. NUCLEAR PHYSICS/ASTROPHYSICS
452
C. F. Maguire
/ Non -equilibrium particle emission
momentum deficit. Quite clearly the break-up fusion process described at the end of the last section will result in incomplete momentum transfer but break-up fusion is not as interesting as hot spot production, for example. Two experiments have been done recently that wmbine the techniques of energetic light-particle measurement and resolved heavy-particle velocity spectroscopy. The systems measured were 252 MeV ?ji on &Ca (6 MeV per nucleon above the Coulomb barrier) and 160 MeV 160 on @Ca (7 MeV per nut 1w n above the barrier). For the ‘*Si induced reactions, a 1.1 m timeof-flight (TOF) telescoped analyzed the fusion-evaporation residues, obtaining better than unit mass resolution up to about mass 63, the highest mass remaining from the A = 68 compound nucleus. The centroid velocity for the inclusive residue particles was consistent with no velocity shift coming from less than full momentum transfer. The coincident light-particle multiplicity spectra (figs. 16-19) bear this fact out. Both the proton and the alpha particle multiplicity shapes and magnitudes are very well reproduced by the PACE calculations. No non-equilibrium high-energy particles are discernible, not even an alpha-particle break-up fusion group at beam velocity. What is interesting about this null result is that at the 6 MeV per nucleon above the Coulomb barrier characterizing this system, a substantial nonequilibrium production was evident for the “‘Yb nonequilibrium neutron production (fig. 6) in fusionevaporation residue coincidence. The second system measured, 160 +40Ca, exhibited a 7% momentum deficit for the inclusive residue centroid velocity value. This deficit can be correlated with the existence of non-equilibrium particle production as seen in figs. 20-21, illustrating the proton- and the alphaparticle multiplicity spectra. The PACE predicted spectra are generally able to reproduce the maxmima of these spectra, but towards high energy at forward angles there is too much experimental yield. For the protons, there is apparently a small high-temperature wmponent, with much less strength than the non-equilibrium yield seen in the t60 +93Nb reactions. For the alpha particles, there is also apparently a beam velocity wmponent especially at the 25O light particle observation angle. Again, given the high velocity above the Coulomb barrier, the non-equilibrium yield for this reaction does not compare with the systematics seen in the “‘Yb production. Granted the low velocity source seen in that experiment, it is possible that the neutrons derived from forward recoiling target nuclei before full momentum transfer took place. For the lighter nuclei considered here, the neutron excess is not as pronounced and the multiplicities are reduced. One wmes once more to the conclusion that in non-equilibrium production several different processes are responsible.
5. Summary and conclusions
Non-equilibrium particle production has been studied in coincidence with fusion-evaporation residue detection, corresponding to near full momentum, central collisions taking place. These data, when analyzed in terms of moving source model parameters, yield very different values for the temperature and the source velocities. In some, cases, such as non-equilibrium experiments on heavy targets, the source appears to be the target system prior to fusion. For 160 +93Nb at 206 MeV, the source seems to be the projectile, again prior to fusion. There is also a great difference in the magnitude of the non-equilibrium particle production, again the heavy-target neutron experiments being more prolific. At comparable energies above the Coulomb barrier, experiments on 40Ca have shown only small or no non-equilibrium production. It is clear that one has now reached the point where the microscopic nucleon-nucleon interactions will have to be addressed in order to understand these variations in non-equilibrium particle production. It is a pleasure to acknowledge the contributions of Drs Glenn Young, Terry Awes and F. Plasil of Oak Ridge National Laboratory, and Drs Dermis Kovar, Gunther Rosner and Hiroshi Ikezoe of Argonne National Laboratory for their contributions to this study. Research at Vanderbilt University is supported in part by U.S.D.O.E. grant No. DE-ASO576ER05034.
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