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Azimuthal correlations between light particles emitted in 12O induced reactions on 12C and 197Au at 400 MeV
Volume
148B, number
PHYSICS
4,s
LETTERS
29 November
AZIMUTHAL CORRELATIONS BETWEEN LIGHT PARTICLES IN I60 INDUCED REACTIONS ON ‘*C AND ?Au AT 400 MeV * M.B. TSANG, National
W.G. LYNCH,
Superconducting
Qclotron
C.B. CHITWOOD, Laboratory,
D.J. FIELDS,
1984
EMITTED
D.R. KLESCH,
C.K. GELBKE
Michigan State Uniuersity, Ea.vt Lansing, MI 48824, USA
and G.R. YOUNG,
T.C. AWES, R.L. FERGUSON,
F.E. OBENSHAIN,
F. PLASIL
and
R.L. ROBINSON Oak Ridge National Laboratoty, Received
Oak Ridge, TN 37831, USA
1 June 1984
Azimuthal correlations between light particles emitted to polar angles of 40 and 70 degrees with respect to the beam axis were measured for I60 induced reactions on I2 C and t9’Au at 400 MeV. Coincident light particles are preferentially emitted in a plane which contains the beam axis. For reactions on i* C , coincident light particles are preferentially emitted to opposite sides of the beam axis. These correlations may be understood in terms of the phase space constraints imposed by momentum conservation on systems with finite number of nucleons. For reactions on i9’Au , on the other hand, preferential emission of coincident deuterons and tritons to the same side of the beam axis may be caused by the shadowing of preequilibrium particles by the adjacent cold spectator nuclear matter.
For intermediate energy nuclear collisions, particle emission prior to the attainment of full statistical equilibrium of the emitting nucleus is expected to provide information about the early stages of the reaction. The global trends of single particle inclusive cross sections can be rather well described in terms of the concept of local statistical equilibrium [l-3]. Recent results from two-proton correlation measurements at small relative momenta are consistent with the emission of energetic light particles from a localized region of high excitation [4]. Additional information about the dynamical and geometrical aspects of the reaction may be obtained from investigations of light particle correlations. In order to search for such dynamical correlations and to assess the *
Research sponsored jointly by the National Science Foundation under Grant No. PHY 83 12245 and by the Division of High Energy and Nuclear Physics, US Department of Energy, under contract DE-AC05840R21400 with Martin Marietta Energy Systems, Inc.
0370-2693/84/$ (North-Holland
03.00 0 Elsevier Science Publishers Physics Publishing Division)
importance of phase space constraints for small nuclear systems we have measured azimuthal angular correlations between energetic light particles emitted in 160 induced reactions on a light (‘*C) and a heavy (‘97Au) target at an incident energy of 400 MeV. The experiment was performed at the Holifield Heavy-Ion Research Facility of Oak Ridge National Laboratory. ‘*C and ‘97Au targets of 2.5 and 9.7 mg/cm* areal density were bombarded with 160 ions of 400 MeV incident energy. Prescaled singles and coincident light particles (p, d, t) were detected using seven telescopes with solid angles between 13 and 40 msr. Three of these telescopes were mounted at the polar angles measured with respect to the beam axis of 8 = 40”, 70”, and 130” and the azimuthal angle of 0”; the remaining four telescopes were positioned at the polar angles of 6 = 40”, 70”, 130°, and 160”; their azimuthal angle was varied between 50° and 180°. Absolute cross sections, accurate to lo%%,were obtained from the integrated beam current, the target B.V.
265
Volume
148B, number 43
PHYSICS LETTERS
25 MeV
‘700
-MS 0
50
100
J
50
1I
100
E CM%, Fig. 1. Inclusive light particle cross sections measured for i6 0 induced reactions on 19’Au (left-hand side) and ‘*C (right-hand side) at 400 MeV incident energy. For reactions on 19’Au, estimated upper limits for contributions from compound nucleus evaporation are shown by the solid lines. The solid, dashed and dot-dashed curves are explained in the text.
thickness, and the solid angles of the telescopes. Energy calibrations accurate to 3% were obtained by measuring the energies of recoil protons backscattered from a Mylar target by a 200 MeV 160 beam. Fig. 1 shows the inclusive energy spectra of protons, deuterons, and tritons detected at 8 = 40” and 70”. For reactions induced on 197Au,estimated upper limits for emission from the compound nucleus (CN) are shown by the solid lines in the left-hand part of the figure. These estimates were obtained by assuming that the energy spectra measured at 8 = 160” are entirely due to isotropic evaporation from the compound nucleus. The energy spectra at 40” and 70’ are clearly dominated by non-compound emission processes. For reactions on 12C, on the other hand, the shapes of the energy spectra are consistent with evaporation from the compound nucleus. In order to reduce systematic errors, the azimuthal correlation is defined by the ratio of the coincidence cross section divided by the singles cross sections uX,,/uXu,,.A low energy threshold of 266
29 November
1984
36 MeV was applied in computing the cross section. For reactions on r9’Au, that threshold strongly reduces contributions from compound nucleus decay. Fig. 2 shows the azimuthal correlations of two coincident light particles emitted at t9 = 40” and 70’. For reactions on 12C, there is a clear enhancement for the emission of two coincident light particles to opposite sides of the beam axis, fig. 2a. These correlations may be understood in terms of the phase space constraints imposed by momentum conservation [5]. To illustrate the effect of momentum conservation, we performed schematic calculations [5] for a source (MS) of A, = 28 nucleons and temperature T = 7.1 MeV moving with the velocity of the compound nucleus, u0 = 0.13~. In these calculations, the entire residual source is assumed to recoil after the emission of the first particle to conserve total linear momentum. As is shown by the solid lines on the right-hand side of fig. 1 and in fig. 2a, these schematic calculations reproduce the overall trends of the data rather well indicating that the preferential emission of coincident light particles to opposite sides of the beam axis may be explained in terms of the phase space constraints imposed by momentum conservation on finite nuclear systems. Entirely different azimuthal correlations are observed for reactions on 197Au, fig. 2b. These correlations are nearly left-right symmetric about the beam axis and exhibit a characteristic “V’‘-shape corresponding to the preferential emission of energetic light particles in a plane which contains the beam axis. Close inspection of the coincidence cross sections at +X = 0” and 180” shows a small enhancement for the emission of coincident protons to opposite sides of the beam axis. Coincident deuterons and tritons, on the other hand, are preferentially emitted to the same side of the beam axis. The preferential emission of coincident light particles in a plane containing the beam axis is consistent with the recent observation [6] that non-compound light particles are preferentially emitted in the entrance channel scattering plane (defined as the plane which contains the beam axis and which is perpendicular to the semiclassical orbital angular momentum vector for the relative motion between the projectile and target nuclei).
Volume
148B, number
4.5
PHYSICS
LETTERS
29 November
1984
1”1”1’1”~““1”1”~‘~“~“~‘~“,“,
o,5-_A(‘60,
xyl,
b- . Xx-P
ELAB/A=25
t
-r
0.5 -/
x=p
y=d
Id
_ a) A= 12C
MeV,
t
T
::Ji
61,=40”,
8,=70”,
t
x=p
,fr
y=+
+
:rJ,
Ex,y=36-120MeV
x-d
At
y=d d T
+
“J
y=+
’
:
-.
: 14 OO I 1 1SO I I 1180 I -- 0I 1 1SO I , I 180 I -- 0, , , soI I , 180 , -- 0, , , SO , , , I80 , -- 0, , , so, , , 180 ,-
4 (deg) Fig. 2. Azimuthal angular correlations between coincident light particles emitted at 8 = 40’ and 70’ with respect to the beam axis for l6 0 induced reactions on l2 C [(a), lower part] and t9’Au [(b), upper part] at 400 MeV incident energy. A low energy threshold of 36 MeV was applied. See text for explanation of solid and dashed curves.
These observations could be described by assuming the superposition of a collective motion in the reaction plane on the random motion of the individual nucleons. To corroborate this point, we have performed schematic calculations corresponding to emission from a rotating moving source [6]:
which are strongly left-right asymmetric in disagreement with the present data. Approximate agreement with the data may be obtained in terms of two sideways deflected sources d*M,/dE;dG, = d*M,+/dE,‘dQ, + d2MX_/dE;ds2,, where
dzz,:ti (E;, 13,,~$3~) =
const.
x
X
x
J~(iB,(E,m i4b%l-
X exp { - [ E; + E, - 2 E;1’2Eh/2
- Ei sin* 8,
sin* &) “*)
E: sin* 0, sin* +X) “*
(1)
’
where d*MJd E; dS2, is the differential multiplicity for the emission of the light particle X. In ref. [6], purely translational motion was parameter&d in terms of a single sidewards deflected source. Such a parameterization yields cross sections
In eqs. (1) and (2), Ji denotes the first order Bessel function, B, = (2m,)‘/*Rw/T; EC,, = Ei + E, 2( E;E&* cos 8,; E, = $m,v& E, = E; + EC, m,, Ox, and & are the energy, mass, polar angle and azimuthal angle of the emitted particle; R, w, v,, and T are the radius, angular velocity, translational velocity and temperature of the source. The parameter EC is introduced to correct for Coulomb 267
Volume
148B, number
43
PHYSICS
repulsion from the target. Eqs. (1) and (2) parameterize the single particle distributions for a fixed orientation of the entrance channel scattering plane where r& = 0” or 180” correspond to emission in this plane. Single particle spectra are obtained after averaging over the orientation of this plane,
= const.
2Td@ J0
To compare with the experimental azimuthal correlation, both the singles and coincidence cross sections are given by ax = const.
(4 and uXY = const.
respectively. The calculations with the rotating hot source parameterisation (RHS) are shown by the dashed curves in fig. 1 and the solid curves in fig. 2b; they were performed with the parameters T = 5.6 MeV, u. = O.O9c, EC = 10 MeV, and Rw = 0.1~. The calculations for two sidewards moving sources (SMS) are shown by the dot-dashed curves in fig. 1 and the dashed curves in fig. 2a; they were performed with the parameters T = 6 MeV, u. = O.l2c, E, = 10 MeV, and 13,= 35”. Both of these schematic calculations can reproduce the overall trends of the azimuthal correlations rather well. 268
LETTERS
29 November
1984
Except at very forward angles, the emission of energetic light particles is largely associated with fusion-like reactions [6,7] in which the major part of the projectile is absorbed by the target nucleus. Therefore, the above parameterisations must not be interpreted in terms of the emission from one or two hot sources which exist separately from the composite system. In particular, the two source parameterisation should not be interpreted in terms of the sequential decay of excited projectile and target residues. We introduce these parameterisations solely to illustrate the effects which may arise from the superpositions of random and ordered velocity components. The relative success of the two parameterisations may be understood in terms of the relative importance of these two velocity components. The random component decreases for heavier particles, but the ordered velocity component remains constant. As a consequence heavier particles are more sensitive to the collective motion of the emitting system. Since both of these rather simple parameterisations describe the qualitative trends of the data, it should be clear that they are not unique and that similar agreement may be obtained by other models which superimpose collective and statistical velocity components. To provide a quantitative comparison of the cross sections corresponding to the emission of coincident light particles to the same (& = 0“) and to opposite (A = 180’) sides of the beam axis, fig. 3 shows the ratios of these coincidence cross sections, a,,(& = 180°)/~Xy(~X = 0’). For reactions on 197Au, this ratio decreases with increasing mass of the two coincident light particles, in contrast to the strong increase measured for reactions on 12C. The dot-dashed and dashed lines in the figure illustrate the effects due to momentum conservation for the case that the momentum of the emitted particle is shared by A, = 28 and A, = 40,60,90,213 nucleons, respectively. (The number A, should not be identified with the number of “participant” nucleons since momentum may also be transferred to the cold spectator matter.) For these calculations, particles were assumed to be emitted with maxwellian distributions corresponding to a temperature of T = 7.1 MeV and initial mean velocity parallel to the beam axis of ua = 0.13~ (dot-dashed line) and
Volume
148B, number
45
PHYSICS
. .
J
A(‘lsO (1x y) I E/A= 8, = 400, By = 700
25MeV
.‘28 /
Ex=Ey=36-120MeV 4-
0
A=‘%
0
A= ‘s7A”
/ 40
o/.--’ /’ cc
60
d-C - 90
__-_-
- --
213
0 l
b) x=d 1
I
2
3
Fig. 3. Ratio of cross sections corresponding to emission of coincident light particles to opposite sides and to the same side of the beam axis for I60 induced reactions on “C (open points) and ‘97Au (full points) at 400 MeV incident energy. The dashed and dot-dashed curves illustrate the effects of momentum conservation for systems with finite number of nucleons. The calculations are explained in the text.
u0 = 0.11~ (dashed lines). After the emission of a particle of mass number A, and velocity u,, the mean velocity of the second particle was assumed to be changed by Au,, = A,u,/(A, - A,). (The parameters for the source consisting of A, = 28 nucleons are identical with the parameters used for the calculations shown in fig. 2a.) Qualitatively, the ratios a,,($ = 180°)/uX, (+ = 0”) might be explained in terms of the competing effects caused by shadowing [8-lo], and momentum conservation although different interpretations may be possible. If preequilibrium emission originates from a localized region of high excitation [4], absorption or rescattering by the adjacent spectator nuclear matter will enhance emission to the same side of the beam axis. Momentum conservation, on the other hand, will favor emission to opposite sides of the beam axis.
LETTERS
29 November
1984
Whether coincident light particles are preferentially emitted to the same or to opposite sides of the beam axis will depend on the relative magnitude of these two opposing effects. Absorptive effects are expected to be more pronounced for the emission of composite light particles than for the emission of nucleons. This is in qualitative agreement with the trends measured for reactions on 19’Au where it is observed that coincident protons have a slight preference to emerge at opposite sides of the beam axis, whereas coincident composite light particles have a slight preference to emerge at the same side of the beam axis. In summary, we have measured the azimuthal angular correlations between light particles emitted at 8 = 40” and 70” with respect to the beam axis for 160 induced reactions on ‘*C and 19’Au at 400 MeV incident energy. For reactions on 12C, the observed preferential emission of two coincident light particles to opposite sides of the beam axis may be understood in terms of the phase space constraints imposed by momentum conservation on systems with finite number of nucleons. For reactions on 19’Au, non-compound light particles are preferentially emitted in a plane containing the beam axis. This is consistent with an ordered motion in a direction perpendicular to the entrance channel orbital angular momentum which is superimposed onto the random motion of the individual light particles [6]. The small enhancements for the emission of two coincident protons to opposite sides of the beam axis and for the emission of two composite light particles to the same side of the beam axis might result from the competition of momentum conservation effects and absorptive (shadowing) effects. References 111 T.C. Awes et al., Phys. Lett. 103B (1981) 417.
PI T.C. Awes et al., Phys. Rev. C25 (1982) 2361. 131 G.D. Westfall et al., Phys. Lett. 116B (1982) 118. 141 W.G. Lynch et al., Phys. Rev. Lett. 51 (1983) 1850. [51 W.G. Lynch et al., Phys. Lett. 108B (1982) 274. t61 M.B. Tsang et al., Phys. Rev. Lett. 52 (1984) 1964. [71 T.C. Awes et al., Phys. Rev. C24 (1981) 89. and M. Westrom, Nucl. Phys. A314 181 P.A. Gottschalk (1979) 232. [91 I. Tanihata et al., Phys. Lett. 97B (1980) 363. Phys. Rev. C29 (1984) 139. WI W.A. Friedman,
269
148B, number
PHYSICS
4,s
LETTERS
29 November
AZIMUTHAL CORRELATIONS BETWEEN LIGHT PARTICLES IN I60 INDUCED REACTIONS ON ‘*C AND ?Au AT 400 MeV * M.B. TSANG, National
W.G. LYNCH,
Superconducting
Qclotron
C.B. CHITWOOD, Laboratory,
D.J. FIELDS,
1984
EMITTED
D.R. KLESCH,
C.K. GELBKE
Michigan State Uniuersity, Ea.vt Lansing, MI 48824, USA
and G.R. YOUNG,
T.C. AWES, R.L. FERGUSON,
F.E. OBENSHAIN,
F. PLASIL
and
R.L. ROBINSON Oak Ridge National Laboratoty, Received
Oak Ridge, TN 37831, USA
1 June 1984
Azimuthal correlations between light particles emitted to polar angles of 40 and 70 degrees with respect to the beam axis were measured for I60 induced reactions on I2 C and t9’Au at 400 MeV. Coincident light particles are preferentially emitted in a plane which contains the beam axis. For reactions on i* C , coincident light particles are preferentially emitted to opposite sides of the beam axis. These correlations may be understood in terms of the phase space constraints imposed by momentum conservation on systems with finite number of nucleons. For reactions on i9’Au , on the other hand, preferential emission of coincident deuterons and tritons to the same side of the beam axis may be caused by the shadowing of preequilibrium particles by the adjacent cold spectator nuclear matter.
For intermediate energy nuclear collisions, particle emission prior to the attainment of full statistical equilibrium of the emitting nucleus is expected to provide information about the early stages of the reaction. The global trends of single particle inclusive cross sections can be rather well described in terms of the concept of local statistical equilibrium [l-3]. Recent results from two-proton correlation measurements at small relative momenta are consistent with the emission of energetic light particles from a localized region of high excitation [4]. Additional information about the dynamical and geometrical aspects of the reaction may be obtained from investigations of light particle correlations. In order to search for such dynamical correlations and to assess the *
Research sponsored jointly by the National Science Foundation under Grant No. PHY 83 12245 and by the Division of High Energy and Nuclear Physics, US Department of Energy, under contract DE-AC05840R21400 with Martin Marietta Energy Systems, Inc.
0370-2693/84/$ (North-Holland
03.00 0 Elsevier Science Publishers Physics Publishing Division)
importance of phase space constraints for small nuclear systems we have measured azimuthal angular correlations between energetic light particles emitted in 160 induced reactions on a light (‘*C) and a heavy (‘97Au) target at an incident energy of 400 MeV. The experiment was performed at the Holifield Heavy-Ion Research Facility of Oak Ridge National Laboratory. ‘*C and ‘97Au targets of 2.5 and 9.7 mg/cm* areal density were bombarded with 160 ions of 400 MeV incident energy. Prescaled singles and coincident light particles (p, d, t) were detected using seven telescopes with solid angles between 13 and 40 msr. Three of these telescopes were mounted at the polar angles measured with respect to the beam axis of 8 = 40”, 70”, and 130” and the azimuthal angle of 0”; the remaining four telescopes were positioned at the polar angles of 6 = 40”, 70”, 130°, and 160”; their azimuthal angle was varied between 50° and 180°. Absolute cross sections, accurate to lo%%,were obtained from the integrated beam current, the target B.V.
265
Volume
148B, number 43
PHYSICS LETTERS
25 MeV
‘700
-MS 0
50
100
J
50
1I
100
E CM%, Fig. 1. Inclusive light particle cross sections measured for i6 0 induced reactions on 19’Au (left-hand side) and ‘*C (right-hand side) at 400 MeV incident energy. For reactions on 19’Au, estimated upper limits for contributions from compound nucleus evaporation are shown by the solid lines. The solid, dashed and dot-dashed curves are explained in the text.
thickness, and the solid angles of the telescopes. Energy calibrations accurate to 3% were obtained by measuring the energies of recoil protons backscattered from a Mylar target by a 200 MeV 160 beam. Fig. 1 shows the inclusive energy spectra of protons, deuterons, and tritons detected at 8 = 40” and 70”. For reactions induced on 197Au,estimated upper limits for emission from the compound nucleus (CN) are shown by the solid lines in the left-hand part of the figure. These estimates were obtained by assuming that the energy spectra measured at 8 = 160” are entirely due to isotropic evaporation from the compound nucleus. The energy spectra at 40” and 70’ are clearly dominated by non-compound emission processes. For reactions on 12C, on the other hand, the shapes of the energy spectra are consistent with evaporation from the compound nucleus. In order to reduce systematic errors, the azimuthal correlation is defined by the ratio of the coincidence cross section divided by the singles cross sections uX,,/uXu,,.A low energy threshold of 266
29 November
1984
36 MeV was applied in computing the cross section. For reactions on r9’Au, that threshold strongly reduces contributions from compound nucleus decay. Fig. 2 shows the azimuthal correlations of two coincident light particles emitted at t9 = 40” and 70’. For reactions on 12C, there is a clear enhancement for the emission of two coincident light particles to opposite sides of the beam axis, fig. 2a. These correlations may be understood in terms of the phase space constraints imposed by momentum conservation [5]. To illustrate the effect of momentum conservation, we performed schematic calculations [5] for a source (MS) of A, = 28 nucleons and temperature T = 7.1 MeV moving with the velocity of the compound nucleus, u0 = 0.13~. In these calculations, the entire residual source is assumed to recoil after the emission of the first particle to conserve total linear momentum. As is shown by the solid lines on the right-hand side of fig. 1 and in fig. 2a, these schematic calculations reproduce the overall trends of the data rather well indicating that the preferential emission of coincident light particles to opposite sides of the beam axis may be explained in terms of the phase space constraints imposed by momentum conservation on finite nuclear systems. Entirely different azimuthal correlations are observed for reactions on 197Au, fig. 2b. These correlations are nearly left-right symmetric about the beam axis and exhibit a characteristic “V’‘-shape corresponding to the preferential emission of energetic light particles in a plane which contains the beam axis. Close inspection of the coincidence cross sections at +X = 0” and 180” shows a small enhancement for the emission of coincident protons to opposite sides of the beam axis. Coincident deuterons and tritons, on the other hand, are preferentially emitted to the same side of the beam axis. The preferential emission of coincident light particles in a plane containing the beam axis is consistent with the recent observation [6] that non-compound light particles are preferentially emitted in the entrance channel scattering plane (defined as the plane which contains the beam axis and which is perpendicular to the semiclassical orbital angular momentum vector for the relative motion between the projectile and target nuclei).
Volume
148B, number
4.5
PHYSICS
LETTERS
29 November
1984
1”1”1’1”~““1”1”~‘~“~“~‘~“,“,
o,5-_A(‘60,
xyl,
b- . Xx-P
ELAB/A=25
t
-r
0.5 -/
x=p
y=d
Id
_ a) A= 12C
MeV,
t
T
::Ji
61,=40”,
8,=70”,
t
x=p
,fr
y=+
+
:rJ,
Ex,y=36-120MeV
x-d
At
y=d d T
+
“J
y=+
’
:
-.
: 14 OO I 1 1SO I I 1180 I -- 0I 1 1SO I , I 180 I -- 0, , , soI I , 180 , -- 0, , , SO , , , I80 , -- 0, , , so, , , 180 ,-
4 (deg) Fig. 2. Azimuthal angular correlations between coincident light particles emitted at 8 = 40’ and 70’ with respect to the beam axis for l6 0 induced reactions on l2 C [(a), lower part] and t9’Au [(b), upper part] at 400 MeV incident energy. A low energy threshold of 36 MeV was applied. See text for explanation of solid and dashed curves.
These observations could be described by assuming the superposition of a collective motion in the reaction plane on the random motion of the individual nucleons. To corroborate this point, we have performed schematic calculations corresponding to emission from a rotating moving source [6]:
which are strongly left-right asymmetric in disagreement with the present data. Approximate agreement with the data may be obtained in terms of two sideways deflected sources d*M,/dE;dG, = d*M,+/dE,‘dQ, + d2MX_/dE;ds2,, where
dzz,:ti (E;, 13,,~$3~) =
const.
x
X
x
J~(iB,(E,m i4b%l-
X exp { - [ E; + E, - 2 E;1’2Eh/2
- Ei sin* 8,
sin* &) “*)
E: sin* 0, sin* +X) “*
(1)
’
where d*MJd E; dS2, is the differential multiplicity for the emission of the light particle X. In ref. [6], purely translational motion was parameter&d in terms of a single sidewards deflected source. Such a parameterization yields cross sections
In eqs. (1) and (2), Ji denotes the first order Bessel function, B, = (2m,)‘/*Rw/T; EC,, = Ei + E, 2( E;E&* cos 8,; E, = $m,v& E, = E; + EC, m,, Ox, and & are the energy, mass, polar angle and azimuthal angle of the emitted particle; R, w, v,, and T are the radius, angular velocity, translational velocity and temperature of the source. The parameter EC is introduced to correct for Coulomb 267
Volume
148B, number
43
PHYSICS
repulsion from the target. Eqs. (1) and (2) parameterize the single particle distributions for a fixed orientation of the entrance channel scattering plane where r& = 0” or 180” correspond to emission in this plane. Single particle spectra are obtained after averaging over the orientation of this plane,
= const.
2Td@ J0
To compare with the experimental azimuthal correlation, both the singles and coincidence cross sections are given by ax = const.
(4 and uXY = const.
respectively. The calculations with the rotating hot source parameterisation (RHS) are shown by the dashed curves in fig. 1 and the solid curves in fig. 2b; they were performed with the parameters T = 5.6 MeV, u. = O.O9c, EC = 10 MeV, and Rw = 0.1~. The calculations for two sidewards moving sources (SMS) are shown by the dot-dashed curves in fig. 1 and the dashed curves in fig. 2a; they were performed with the parameters T = 6 MeV, u. = O.l2c, E, = 10 MeV, and 13,= 35”. Both of these schematic calculations can reproduce the overall trends of the azimuthal correlations rather well. 268
LETTERS
29 November
1984
Except at very forward angles, the emission of energetic light particles is largely associated with fusion-like reactions [6,7] in which the major part of the projectile is absorbed by the target nucleus. Therefore, the above parameterisations must not be interpreted in terms of the emission from one or two hot sources which exist separately from the composite system. In particular, the two source parameterisation should not be interpreted in terms of the sequential decay of excited projectile and target residues. We introduce these parameterisations solely to illustrate the effects which may arise from the superpositions of random and ordered velocity components. The relative success of the two parameterisations may be understood in terms of the relative importance of these two velocity components. The random component decreases for heavier particles, but the ordered velocity component remains constant. As a consequence heavier particles are more sensitive to the collective motion of the emitting system. Since both of these rather simple parameterisations describe the qualitative trends of the data, it should be clear that they are not unique and that similar agreement may be obtained by other models which superimpose collective and statistical velocity components. To provide a quantitative comparison of the cross sections corresponding to the emission of coincident light particles to the same (& = 0“) and to opposite (A = 180’) sides of the beam axis, fig. 3 shows the ratios of these coincidence cross sections, a,,(& = 180°)/~Xy(~X = 0’). For reactions on 197Au, this ratio decreases with increasing mass of the two coincident light particles, in contrast to the strong increase measured for reactions on 12C. The dot-dashed and dashed lines in the figure illustrate the effects due to momentum conservation for the case that the momentum of the emitted particle is shared by A, = 28 and A, = 40,60,90,213 nucleons, respectively. (The number A, should not be identified with the number of “participant” nucleons since momentum may also be transferred to the cold spectator matter.) For these calculations, particles were assumed to be emitted with maxwellian distributions corresponding to a temperature of T = 7.1 MeV and initial mean velocity parallel to the beam axis of ua = 0.13~ (dot-dashed line) and
Volume
148B, number
45
PHYSICS
. .
J
A(‘lsO (1x y) I E/A= 8, = 400, By = 700
25MeV
.‘28 /
Ex=Ey=36-120MeV 4-
0
A=‘%
0
A= ‘s7A”
/ 40
o/.--’ /’ cc
60
d-C - 90
__-_-
- --
213
0 l
b) x=d 1
I
2
3
Fig. 3. Ratio of cross sections corresponding to emission of coincident light particles to opposite sides and to the same side of the beam axis for I60 induced reactions on “C (open points) and ‘97Au (full points) at 400 MeV incident energy. The dashed and dot-dashed curves illustrate the effects of momentum conservation for systems with finite number of nucleons. The calculations are explained in the text.
u0 = 0.11~ (dashed lines). After the emission of a particle of mass number A, and velocity u,, the mean velocity of the second particle was assumed to be changed by Au,, = A,u,/(A, - A,). (The parameters for the source consisting of A, = 28 nucleons are identical with the parameters used for the calculations shown in fig. 2a.) Qualitatively, the ratios a,,($ = 180°)/uX, (+ = 0”) might be explained in terms of the competing effects caused by shadowing [8-lo], and momentum conservation although different interpretations may be possible. If preequilibrium emission originates from a localized region of high excitation [4], absorption or rescattering by the adjacent spectator nuclear matter will enhance emission to the same side of the beam axis. Momentum conservation, on the other hand, will favor emission to opposite sides of the beam axis.
LETTERS
29 November
1984
Whether coincident light particles are preferentially emitted to the same or to opposite sides of the beam axis will depend on the relative magnitude of these two opposing effects. Absorptive effects are expected to be more pronounced for the emission of composite light particles than for the emission of nucleons. This is in qualitative agreement with the trends measured for reactions on 19’Au where it is observed that coincident protons have a slight preference to emerge at opposite sides of the beam axis, whereas coincident composite light particles have a slight preference to emerge at the same side of the beam axis. In summary, we have measured the azimuthal angular correlations between light particles emitted at 8 = 40” and 70” with respect to the beam axis for 160 induced reactions on ‘*C and 19’Au at 400 MeV incident energy. For reactions on 12C, the observed preferential emission of two coincident light particles to opposite sides of the beam axis may be understood in terms of the phase space constraints imposed by momentum conservation on systems with finite number of nucleons. For reactions on 19’Au, non-compound light particles are preferentially emitted in a plane containing the beam axis. This is consistent with an ordered motion in a direction perpendicular to the entrance channel orbital angular momentum which is superimposed onto the random motion of the individual light particles [6]. The small enhancements for the emission of two coincident protons to opposite sides of the beam axis and for the emission of two composite light particles to the same side of the beam axis might result from the competition of momentum conservation effects and absorptive (shadowing) effects. References 111 T.C. Awes et al., Phys. Lett. 103B (1981) 417.
PI T.C. Awes et al., Phys. Rev. C25 (1982) 2361. 131 G.D. Westfall et al., Phys. Lett. 116B (1982) 118. 141 W.G. Lynch et al., Phys. Rev. Lett. 51 (1983) 1850. [51 W.G. Lynch et al., Phys. Lett. 108B (1982) 274. t61 M.B. Tsang et al., Phys. Rev. Lett. 52 (1984) 1964. [71 T.C. Awes et al., Phys. Rev. C24 (1981) 89. and M. Westrom, Nucl. Phys. A314 181 P.A. Gottschalk (1979) 232. [91 I. Tanihata et al., Phys. Lett. 97B (1980) 363. Phys. Rev. C29 (1984) 139. WI W.A. Friedman,
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