Neutron decay of the excitation-energy region up to 60 MeV, excited by heavy ion scattering. (I) 208Pb

NUCLEAR PHYSICS A WStwiER

Nuclear Physics A 578 (1994) 238-266

eutron decay of the excitation-energy region up to 60 MeV, excited by heavy ion scattering. Zoapb* (I) A.M. van den Berga, D. Chmielewskaa ,1 , J.A. Bordewijka, S . Brandenburg a, A. van der Woude a, Y. Blurnenfeld b, N. Frascaria b, J.C. Roynette b, J.A. Scarpaci b, T. Suomij ârrvi b, N. Alamanos c, F. Auger c, A. Gillibert c, P. Roussel-Chomaz c,2, J. Blomgren d,3, L. Nilsson e, N. Olsson f, R. Turcotte g Kernfysisch Versneller Instituut, 9747 AA Groningen, The Netherlands Ins.Itut de Physique Nucléaire, IN2P3-CNRS 91406 Orsay Cedex, France I CEAIDAPNMISPhN, C.E. Saclay, 91191 Gif-sur-Yvette Cedex, France d Department of Radiation Sciences, Box 533, S-75121 Uppsala, Sweden e The Svedberg Laboratory, Box 533, S-%5121 Uppsala, Sweden f Department o~ Neutron Research, Box 535, S-75121 Uppsala, Sweden g Foster Radiation Laboratoryv, McGill University, Montreal, Canada H3A 2B2 a

b

Received 28 February 1994; revised 2 May 1994

Abstract The neutron decay of the continuum in 208 Pb, excited by small-angle inelastic scattering of 84 Me`1/nucleon 1'O ions in the range from 1 .5° to 4.5°, has been measured. Statistical decay was found to dominate the excitation-energy interval studied, up to 60 MeV In the excitationenergy interval of about 10 to 30 MeV a distinct direct-decay component to the hole states in 207 Pb and a decay pattern resembling pre-equilibrium decay was observed . The angular correlation ofthe l?cle-state population suggests that in addition to tâc direC-t decay to the hole states in 2m pb, there is another, unidentified process populating the same states. Keywords: NUCLEAR REACTIONS 208pb(170'17O1)2°s-xpb, E-= 1428 MeV; measured neutron decay spectrum, angular correlation of hole-state population versus "Pb excitation energy ; 2n8 Pb deduced continutim neutron decay features . Elsevier Science B.V. SSW 03 75-9474 (94) 00271-N

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239

1. Introduction Giant multipole resonances have been studied extensively during the last two decades by inelastic hadron and electron scattering and much information on their energy distributions and strengths has been collected. For a number of resonance modes systematic data for these parameters are available over the entire mass range. This information is summarized in a number of review papers [ 1-4] . A giant resonance is described microscopically as a coherent superposition of one-particle-one-hole (lp-1h) excitations. Microscopic calculations of properties of giant resonances have been performed by several groups using random phase approximation methods involving lp-lh as well as 2p-2h excitations [ 5-7] . These calculations have been fairly successful in accounting

for the energies and strengths of some resonances, like the isoscalar monopole resonance (ISMR), the isovector dipole (IVDR) and the isoscalar quadrupole (ISQR) .

To learn about the detailed structure of giant multipole resonances it is not sufficient to

perform singles-scattering experiments ; the decay of the resonances has to be investigated

as well . During the last decade experiments have been performed, in which particles or y-rays were detected in coincidence with the inelastically scattered projectiles . In such

experiments it is pos: :ble to investigate the structure and the dynamic properties of the giant resonances . The total width of a resonant state can be expressed as a sum of three terms

r=rt +r' +A, rt

(1)

is the escape width representing the coupling of the initial collective lp-lh states to the continuum, is the spreading width associated with the spreading of these states into more complicated states, i.e. 2p-2h, 3p-3h, etc. and d is related to the Landau damping corresponding to fragmentation of the initial lp-lh states. If the where

ri

excitation energy of a giant resonance is above the particle-emission threshold, which in general is the case, the strongest decay channel is particle emission . In heavy nuclei

neutron decay is dominant because of the height of the Coulomb barrier, whereas in light nuclei proton and a-particle decay widths in general are comparable with that for neutron decay. The process in which a collective lp-lh state decays by the emission of one nucleon (i .e . erect decay) populates a hole state in the final nucleus . Alternatively,

the particle or the hole interacts with another nucleon in the target nucleus and creates a 2p-2h state (spreading) . Decay from states of moderate complexity (like np-nh states, where n = 2 or 3) is often referred to as pre-equilibrium decay. The 2p-2h state can undergo further spreading to 3p-3h states and finally :o a completely equilibrated system, the compound nucleus, the decay of which is entirely governed by statistical

considerations . A special case occurs when the particle or the hole couples to a surface * Experiment performed at GANIL. 1 On leave from : Soltan Institute for Nuclear Studies, 05-400 Swierk, Poland . 2 Present address: GANIL, BP 5027, 14021 Caen Cedex, France. 3 Present address: Department of Neutron Research, Uppsala University, Box 535, S-75121 Uppsala, Sweden.

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vibration (quadrupole or octupole) ; decay from the 2p-2h state can then proceed to a hole state coupled to this surface vibration. From the point of view of the nuclear structure the interesting decay modes are the direct and pre-equilibrium processes, because they can give information on the wave function of the giant resonance. Experimentally the direct and pre-equilibrium decay components can be extracted by subtracting the statistical decay part from the total decay. The statistical decay is calculated using the Hauser-Feshbach formalism [8] . Experiments to study the different decay mechanisms have been performed for various resonances. For the ISMR, a-particle scattering through small forward angles (including 0°) and a difference-of-spectra technique have been employed [9-131 . By using these techniques, contributions of other resonances could be eliminated to a large extent . These studies have been performed for a number of heavy and medium-weight closedshell nuclei and the main conclusion was that the decay is predominantly statistical . The non-statistical (direct and pre-equilibrium) decay branch ranges from 5 to 30% in the nuclei investigated so far. In some cases it was possible to distinguish decay to individual (or groups of) final states and the results have been compared to calculations of partial decay widths [ 11, 14,15 ] . An interesting observation in these experimental studies is that the continuum underlying the ISMR also decays partly non-statistically . Also the IVDR in 208Pb decays mainly statistically, although a (y, n) experiment has clearly demonstrated the existence of a direct-decay branch [ 161 . Very few data exist for particle decay of the continuum above the 2huv region. Blumenfeld et al. have studied the proton decay of 4°Ca, excited in an inelastic 4°Ca + 40Ca scattering experiment [ 17-191 . In the excitation-energy interval 30 < Ex < 38 MeV they observed a small but definite excess population of hole states in the residual nucleus 39 K compared to calculations based on a statistical model. In another experiment, the 58Ni(e, e'p) 57 Co reaction has been studied in the excitation-energy range from 2541 MeV, and a (17±~6 ) % decay branch to hole states in 57Co was found [20] . A small non-statistical neutron-decay branch was also found in some A > 90 nuclei in the excitation-energy region a few MeV above the ISMR [9,12,13] . The main purpose of the present experiment was to study the neutron-decay mode of the IVDR region and beyond . Especially the 2hw isovector excitations expected to be located around Ex = 130A -1 /3 as well as the Mw isoscalar dipole and octupole resonances and the double-phonon excitations are of interest . It is clear that if one is searching for structures at a relatively high excitation energy by means of inelastic scattering of hadrons, the contribution of the continuum underlying these resonances has to be taken into account . At least partly, this continuumi is due to pick-up-breakup and knock-out processes [21] . It has been shown previously [9,12,13,17,18] that the contribution from such processes can be reduced if one selects. specific kinematical conditions for detecting the scattered particle in coincidence with a low-energy particle emitted from the excited nucleus. This technique has been used in the present experiment. Pick-up-break-up, i.e. processes like (170,180*), 180* -, 170 + n, give rise to broad peaks in singles spectra at apparent excitation energies around the beam energy per nucleon 1 22], which in our case is far above the region of this study.

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

241

During the last few years it has been recognized that inelastic scattering of intermediate energy (40-100 MeV/nucleon) heavy ions at small scattering angles [23-27] is a powerful tool in the study of giant resonances . The most conspicuous feature of heavy-

ion scattering in this energy domain is t!-e very strong population of the 1VDR by

Coulomb excitation . The resonance-to-continuum ratio is considerably larger than in

light-ion scattering experiments. Another property of the heavy-ion scattering process is that the differential cross section peaks in a narrow angular range at small angles

due in particular to the strong forward peaking of the Coulomb excitation cross section, implying that a magnetic spectrometer covering a solid angle of several msr captures a sizeable fraction of the inelastically scattered ions . In this and the following paper data on the neutron decay of giant resonances in 2°sPb, and in 9°Zr and 124Sn, respectively, excited by small-angle inelastic scattering of 84 MeV/nucleon 170 ions are presented. The experiment has been performed at the GANIL facility, Caen, France . An introduction to the field, general motivations for the experiment, a description of the experimental methods and calculation techniques are given in this paper (1) . Data on 2°8Pb are presented here, while the corresponding data on 124S

n are presented in paper (U), i.e . Ref. [28] . In addition, some preliminary 2°8Pb have already been presented [291 . This paper is organized as follows: results on Section 2 contains a description of the experimental set-up and data reduction . In the

9°Zr and

next section the experimental results and the statistical decay calculations are described. These statistical calculations are compared with the data in Section 4, emanating in a discussion in Section 5, and summary in Section 6, which also contains the conclusions.

2. Experimental techniques and data reduction 2°8Pb. In the experiment 84 MeV/nucleon 17 0 ions were inelastically scattered from The 17 0 beam was obtained from the GANIL accelerator facility. The emittance and the

energy of the beam were defined by a 270° analyzing system (a-spectrometer) . The momentum analysis of the scattered ions was performed by means of the spectrometer SPEG [301, which was operated in the energy-loss mode. The decay neutrons were

detected by liquid scintillation detectors. The experimental set-up is shown in Fig. 1 and is described in detail in Ref. [311 . A summary of the most important aspects of the experimental equipment and procedure is given below. 2.1 . Heavy-ion detection The spectrometer SPEG was positioned at a scattering angle of 3° . A self-supporting 2°sPb (5 .5 mg/cm2 thick and with an isotopic purity of 99%) was mounted in target of MeV/nucleon, the SPEG target chamber. The 1708+ beam energy was 1428 MeV, i.e . 84 (FWHM), in and had an intensity of 1 to 2 enA. The energy resolution, 800 keV nucleus, was the spectra of scattered 17 0 ions, i.e . i=. excitation energy of the target the exit dominated by energy-loss straggling ir_- the target. The beam was stopped near

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A.M. van den Berg et al./Nuclear Physics A 578 (1994) 238-266

Scattered particles

13

i

Recoiling nuclei

0

Target

D 0

00 ö-

-

im

I rc i dent

beam

Fig. 1. Overview of the position of the neutron detectors relative to each other and to the beam direction at the target position .

of the first dipole of SPEG. Calibration of the magnetic rigidity and the dispersion was performed by elastic scattering of 170 ions and by the neutron-transfer reaction 208Pb ( 170,160) 209pb.

Two position-sensitive 'Ptectors (drift chambers), located close to the focal plane, were used to reconstruct the position mid direction of the scattered ions at the focalplane. During the data taking of coincident events the elastically scattered particles were prevented from hitting the focal-plane detector system by inserting a movable finger in front of it. A plastic scintillator, positioned downstream of the second drift chamber, and viewed from both ends by photomultiplier tubes, served as the trigger detector and gave the start signal for the time-of-flight (TOF) measurement of the particle trajectory through the spectrometer. A signal generated from the cyclotron radio-frequency system was used as the stop pulse in this TOF measurement . Particle identification was accomplished by combining this TOF information and a measurement of the energy loss in an ionization chamber, mounted between the second drift chamber and the plastic scintillator. To calibrate the emi :bdon angle of the scattered ions a sieve in front of the aperture of the spectrometer and a wire target were used. Using this dedicated set up a calibration measurement was performed of which the data for elastic and inelastic scattering were recorded for further analysis. 2.2. Neutron detection

In the neutron decay studies four large (30 cm diameter and 5 cm thick) detectors were used, positioned at a distance of about 186 cm from the target and at 91", 103° ,

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

243

-50 -60

v

-80

-90

0

20

40

60

Ex (MeV) Fig. 2. The angle 04 of the recoiling nuclei as a function of the scattering angle e3 and the excitation energy of the target nucleus. 116° and 129 ° with respect to the beam direction, i.e. at backward angles with respect

to the direction of the recoiling target nucleus . The angle 04 of the recoiling nucleus with respect to the beam direction is shown in Fig. 2 for three selected values of the scattering angle of the 17 0 ions: 03 = 1 .5°, 2.5 ° and 4.5°. With the aim of studying the angular distribution of the emitted neutrons seven smaller detectors were positioned at

various other angles (see Fig. 1 and Table 1) . The pulse height of the anode signals from the neutron detectors was calibrated before and after the data-taking period for each

target using a 22 Na source . Using these calibrations a software threshold of 100 keV,,. (electron equivalent) was defined, corresponding to a neutron-energy threshold of about

0.6 MeV

The neutron energy was calculated from the neutron time of flight. The stop signal

for the time-of-flight measurement was derived from the anode signal of the photomultiplier tube viewing the scintillator. The start signal was obtained from an overlap

of a signal derived from the accelerator radio-frequency system with a fast timing

signal obtained from the read-out of the plastic scintillator mounted near the focalplane detector. The stability of the arrival time of the beam bunches at the target with

respect to the accelerator radio-frequency system was monitored using a small plastic scintillator mounted on top of the scattering chamber. During the entire data-taking period the short-term (i .e . 8 h) stability was found to be better than I ns . Pulse-shape discrimination was used to distinguish neutrons from y-radiation [321 (see Fig. 3) . The total time resolution (FWHM) in the neutron TOF measurements was about 2 ns . The time range of the time-to-digital converters (TDC) was 500 ns . True and random

coincidence events were obtained from windows set ;n these TOF spectra as indicated in Fig. 3. To compare the absolute efficiency of each detector a calibration measurement

244

A.M. van den Berg et al./Nuclear Physics A 578 (1994) 238-266

Table 1 Relative positions of the neutron detectors 8n (°)

Thickness 1 (cm)

Diameter D (cm)

Flight path L (cm)

-162 -137 -76 78 91 103 116 129 139 149 e

7 .5 5.0 7.5 7.5 5.0 5.0 5.0 5.0 5.0 5.0 7 .5

12 .5 20.0 12 .5 12 .5 30.0 30 .0 30 .0 30 .0 17 .5 20 .0 12 .5

153 186 153 184 184 185 188 186 182 184 104

EMI

10 11 10 7 26 25 24 25 9 11 21

a

S'cl b

Wiel c

9 8 6 8 28 27 23 22 11

7 8 10 6 29 23 25 24 10 8 19

d

20

a

Relative efficiency with E = vID2/4L2; estimated error is about 5%. ti Relative weighting factors determined with a source; estimated error is about 10%; see text. Relative weighting factors determined from decay; estimated error is about 10%; see text. d No data. e Out of plane.

using an AmBe source was performed, where the source was placed at the target position. 2.3. Data acquisition The data-acquisition system used a Modcomp Classic computer linked to CAMAC electronics through a microprocessor. A logic signal, generated from the coincidence between the plastic scintillator positioned downstream of the SPEG focal plane and an event from any of the neutron detectors or a down-scaled SPEG event, initiated a readout of the CAMAC modules. In addition to coincidences between SPEG and a neutron detector, down-scaled singles events in SPEG were recorded to monitor the population of excited states . Preliminary spectra and detector information were monitored on-line during data taking . All information was stored on magnetic tape for subsequent off-line analysis . The dead time in the data-acquisition system ranged from 20 to 25%. The event-by-event data have been reduced in two steps, using the computer code PAX [33] . In the first step the data were split into separate output streams for SPEG events in coincidence with each neutron detector. In this step data streams were also generated for SPEG events in coincidence with more than one neutron detector and for down-scaled singles from the SPEG detector. In the subsequent step of the analysis, the data were treated for each of the data streams separately. The large mass of the projectile implies that the kinematical conditions of the scattering process differs considerably over the range of scattering angles . Therefore kinematic calculations were performed on an event-by-event basis.

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

245

10 3

10 2

C (0 U w C

10 3

10 2

O U

10 3

10 2 0

400

800

time of flight (channel number)

Fig. 3. (a) The time-of-flight signal for neutrons and y-radiation detected in coincidence with scattered 170 ions in the spectrometer. By analyzing the shape of the pulses from the detectors events induced by neutrons (b) and by y-radiation (c) could be separated .

3. Results 3.1. Singles spectra

A data set obtained by scattering the beam on a wire target while the solid angle of the spectrometer was covered with a sieve, has been used to calibrate the horizontal and vertical scattering angles 9 and 0, respectively. The calibration of the angle was checked by plotting the angular distribution for elastic scattering obtained with the spectrometer centered at 3° and -3 °. For both angular settings of the spectrometer

246

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266 50

1

0

2

3

4

5

6

2

3

0 (degrees) N N N M O Ô O

O T vi c

OU

25 b)

20 15 10

-3

-2

-1

0

1

(degrees) 15 10

C)

(degrees) Fig. 4. (a) Spectrum for the horizontal scattering angle 8. (b) Spectrum for the vertical scattering angle 0. (c) As (b) but with the condition 1 .5° < 0 < 4.5°. The lines display the results of a simultaneous fit of the spectrum with two functions: a gaussian-like function centered around 0° (dotted line) and a function N(O) - c/[a + 10 - bI ]' (solid line) .

the shape of the angular distribution is in agreement with optical model calculations for elastic scattering . Figs. 4a and b show the spectra for 0 and rß obtained from the analysis of the down-scaled singles data. The events at an angle 0 of about 0.9° could be due to scattering of the beam on the entrance slit of the spectrometer. This scattering may have caused background in our data set. This is reflected by the tails in the spectrum of the vertical scattering angle 0 (see Fig. 4b) . By applying a gate on 0 from 1 .5° to 4 .5° these tails reduce substantially, but persist for large scattering angles 0 (see Fig. 4c) . To reduce the amount of background events in our analysed data set the solid angle of

A.M. van den Berg et al. !Nuclear Physics A 578 (1994) 238-266

247

102 10' 1001 . -

T v

20 10 0

0

10

20

30

40

50

60

70

E X (MeV) Fig. 5. (a) The excitation-energy spectrum for the reaction 2°sPb(170,I70' )2o8Pb at E = 1428 MeV and 9i ab = 3° . The subtended solid angle is from 1 .5° to 4.5° horizontally, and from -1 .5° to +1 .5° vertically. These limits are indicated in Fig. 3. (b) The excitation-energy as in (a) but gated on events falling within the solid angle subtended from 1 .5 ° to 4.5 ° horizontally, and from 2.5° to 4.0° vertically. (c) The excitation-energy spectrum as in (a) for "true" coincidences .

the spectrometer was limited by software cuts to the central region of the spectrometer: i .e. from 1 .5° to 4 .5° horizontally, and from -1 .5° to +1 .5° vertically. These limits are indicated in Fig. 4. Fig. 5a shows an excitation-energy spectrum for inelastically scattered 170 ions obtained from the analysis of the down-scaled singles data. The cut-off at an excitation energy of about 2 MeV is caused by the movable finger which intercepted elastically scattered ions. This spectrum has a shape similar to spectra obtained before using the same reaction [23,34] . These experiments have revealed that the dominant giant resonance in the angular range of the present experiment is the IVDR, which has a resonance-to-continuum ratio of about three at its centroid. The virtual photon spectrum

248

A.M. van den Berg et al. /Nuclear Physics A

578 (1994) 238-266

is decreasing rapidly with energy, which naeans that the shape of the IVDR is strongly distorted. In addition, wide resonance-like structures were observed [341 in the 1525 MeV region, and a smoothly varying continuum was assumed underlying the giant resonances . To study the background component visible as the tail in Fig. 4c, well outside the normal acceptance of the spectrometer a solid angle was defined by soft-ware cuts, i.e. from 1 .5° to 4.5° horizontally and from 2.5° to 4 .0° vertically. The energy loss for the events with these conditions is shown in Fig. 5b. It shows that the energy loss for this particular instrumental background is peaked at an excitation energy of about 30 MeV. To correct the singles spectrum shown in Fig. 5a for this background component, the tail in the 0 spectrum was fitted with a function having a 1 /02 behaviour for large values of 1,01 . This fit is indicated in Fig. 4c as the solid line . On basis of this fit the background events in the down-scaled singles spectrum (with -1 .5° < 0 < 1.5° ) is estimated to be 2 .7 times the spectrum shown in Fig. 5b (with 2 .5° < ~ < 4.0') . The measured down-scaled singles spectrum was corrected for this effect. The corrected spectrum has been used in the further analysis of the data. Gating on the prompt and random tirne windows of the neutron-time-of-flight spectra (see Fig. 3), it is possible to generate a spectrum which presents the true coincidences . The excitation-energy spectrum for the true coincidences is displayed in Fig. 5c. The cut-off at an excitation energy E,r ;:t: 8 MeV due to the neutron separation energy, is modified by the efficiency of the neutron detectors . 3.2. Alissing-energy spectra The missing energy E, for the 208Pb(17 O, 17O'xn) reaction was determined from the momentum vectors of the scattered 17() ion measured with the magnetic spectrometer and of the coincident neutron. Up to the threshold for two-neutron emission from 2ospb (Ex = 14.1 MeV) the missing energy En, can be related to the final-state energy Ef, in the residual nucleus 207 Pb. For each event the missing energy and the excitation energy in 208 Pb were used to update two-dimensional matrices ; one matrix for random events only and one for prompt events . By subtraction, the matrix for true coincidences was obtained . To study the decay process as a function of the excitation energy in 2°8Pb the excitation energy was binned with a step size of 1 .28 MeV. By gating on a specific bin the decay from this excitation-energy interval can be studied in detail . A few examples are shown in Fig. 6. These missing-energy spectra show a bump which corresponds to the emission of low-energy neutrons from the decaying nuclei, and therefore it moves to higher values of E, with increasing excitation energy in 2°8Pb . This bump is interpreted as being due to statistical decay. The shape of the cut-off at high values of En, is caused by the energy-dependent efficiency of the neutron detectors (see Fig. 7) . The efficiencies of the neutron detectors (see Fig. 7) have been calculated using a Monte Carlo code [35] with the threshold settings as indicated. In the analysis a software threshold of 100 keVee was used . The number of neutrons, measured for e ach

A.Af. van den Berg et al. /Nuclear physics A 578 (1994) 238-266

N O

U

6

B

10

12

Em (MeV)

14

Fig. 6. Missing-energy spectra for the decay from 10 .2 < Ex < 15.4 MeV. The solid lines indicaU t1~c rq-,sults of statistical model calculations assuming J" = l' for the initial states.

detector during calibration using the Awe source, was used as a relative etci~nc.V determination. The relative yield for each detector is listed as the value &, im rab e I . In this table the relative geometrical efficiency Ere, for each detector is listed as v61. Here the geometrical efficiency is defined as the product of the solid angle sA%tcL-jded and the thickness for each detector. Its the final anaiy- :s of the data the relative efr4ci~nc~+ has been calculated using the yield of neutrons stemming from statistical decay (see also Section 3 .3) .

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A.M. van den Berg et al./Nuclear Physics

A 578 (1994) 238-266

0.7

a U

0.6

0) 0.5 U_ 4)

0

0 .4 0.3

U -10) 1 0.2 N

0.0

O

5

10

Er,

15

20

(MeV)

Fig. 7. The calculated efficiency of a 30 cm diameter and 5 cm thick liquid-scintillator neutron detector. The different curves corresponds to the threshold (in keVee ) on the pulse-height signal from these detectors.

3.3. Statistical model calculations Most of the low-energy neutrons meas?,red in the present experiment are assumed to be due to statistical decay of the excited nuclei . The calculations were performed with the code CASCADE [361, which is based on the Hauser-Feshbach formalism. For each of the nuclei involved in the decay cascade, the level density as a function of the excitation energy should be known . Especially near a shell closure the relatively small level density at low excitation energies should be taken into account correctly. The level density for each nucleus in the decay chain was calculated for four different excitation-energy regions, = uch that the density in one region smoothly joins that of the next region . In region 1 the known level scheires for the A = 207, 206, 205 and 204 isotopes of lead, bismuth and mercury up to an excitation energy El were taken from literature (see Refs . [37-39] and Ref. [401, respectively) . The number of levels nt and the energy E, are listed in Table 2. In region 2 from the energy El to the energy E2, the level density increases rapidly and all individual levels are not well known. In this region, level densities were obtained from the back-shifted Fermi gas model using the parameters of Dilg et dl. [ 411, 2J+ 1 exp[2 a(E- d) - J(J+ 1 )/(2u2 )] 24v/2- a-2 al/ 4 (E -,d + t)514 1

where t is the thermodynamic temperature defined by E - d = ate - t. The spin cutoff parameter o- is given by the rigid rotor value 0'ng ;a 0.0150A5/3 t, while the level density parameter a and the back-shift energy 4 are determined from fits to experimental data. The data sets used to get information on these parameters are low-lying levels and

A.M. van den Berg et aL /Nuclear Physics A 578 (1994) 238-266

251

Table 2 Level-density parameters for Pb isotopes Nucleus

Region 1

Region 2

El (MeV)

nl

E2

(MeV)

a2 (MeV -1 )

3.63

21

8.0 8.0

10 .02 10 .32

2.66 1.85 1.73 0.0

19 28 10 0

8.0 8.0 8.0 8.0

12 .08 13 .55 13 .89 13 .82

208pb 207

1?b

206pba 205pb

204pba 203pb a

Region 4 E3

(MeV)

a4 (MeV -1 )

d4 (MeV)

1.80 0.61

30.0 30.0

8.00 8.00

7.89 6.86

1.34 -0.02 0.99 -0.14

30.0 30.0 30 .0 30.0

8.00 8.00 8.00 8 .00

6.60 5.12 5.13 3 .62

42

(MeV)

Interpolated values for a2 and d2 (see text) .

a

where available - the density of s-wave resonances just above the neutron separation energy, studied in neutron capture (or scattering) in the A -1 isotope. For nuclei where the density of s-wave resonances is not accessible to experiments, e.g. when the A - 1 isotope is unstable, values of the a end d parameters were determined using a quadratic interpolation based on the parameters for neighbouring nuclei (taking into account oddeven effects) . In region 4, at an excitation energy greater than E3 = 30 MeV, liquid-drop level densities were used with the level-density parameter a = A/8 [42,43] . In the intermediate region from E2 to E3 the level densities were calculated from extrapolations and interpolations of the ievel densities in regions 2 and 4. The transmission coefficients for the decay channels were calculated using the optical model parameters given as set B by Rapaport et al. [ 44 ] . The calculations were performed assuming J' = 1 - for the decaying state. The value of the spin has only a :Minor influence on the calculated spectra if E.,( 208 M) > 13 MeV (see Section 4.1) . 208Pb was calculated and The energy distribution for neutrons from the decay of weighted with the number of counts in the excitation-energy spectrum in discrete excitation-energy steps of 160 keV These weights were obtained from the downscaled singles spectrum after correction for the instrumental background events (see Section 3.1) . To take into account recoil effects the calculated neutron-energy distributions were transformed to the laboratory frame [45], and folded with the neutron time-of-flight resolution and the calculated efficiency of the neutron detector. The finite resolution in the excitation-energy spectrum k800 keV) was accounted for by performing these calculations in steps of 160 keV, and subsequently adding consecutive calculated 170 energy resolution . As a final step this folded spectrum spectra, weighted with the was transformed back [ 45 ] to the frame of the emitting nucleus resulting in missingenergy spectra which can be compared with the data. Calculations were performed up 208Pb, using the parameters listed in Table 2. By to an excitation energy of 60 MeV in comparing each calculated spectrum with the corresponding data a scaling factor was obtained, with the condition that the calculated spectt um should not overshoot the data -

in any region .

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A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

-0.8

N c

0.6

-0 0.4 + +++++H++' .++~+

0.0 1 0

10 20 30 40 50 60 70 EX

(MeV)

Fig. 8. The scaling factor R as a function of the excitation energy.

For each neutron detector the scaling factor was determined separately. However, the scaling factor of a particular neutron detector relative to another one should not change as a function of the excitation energy of the initial state. Therefore for each excitationenergy one common scaling factor R was determined for all neutron detectors and fixed weighting factors were used to account for the different detection efficiencies of the individual neutron detectors (see Fig. 8) . These weighting factors Wiel were determined from the comparison of the calculated statistical-decay spectra with the data for several excitation-energy regions (e .g. from 15 to 20 MeV and from 40 to 60 MeV in 208Pb) and are listed in Table 1 . It is seen from this table that for most of the neutron detectors this factor agrees with the relative geometrical efficiency Erej and with the relative yield S,,l as determined from the measurement with the AmBe source . Systematic deviations between the three different factors of about 20% are introduced easily due to the small gain drifts of the anode; signals of the photo-multiplier tubes. It was concluded t:.at the statistical decay is isotropic, within the errors of these data. Therefore, the factor Wrej was found to be a reasonable measure of the different geometrical efficiencies of the neutron detectors for a given (range of the) neutron energy.

.

Comparison with data

4.1. Decay from the 10 < Ex < 15 MeV region In the excitation-energy region below about 13 MeV in 2°8Pb the distinction between statistical and non-statistical decay cannot easily be made . In this domain all decay neutrons have an energy of less than 6 MeV Therefore direct and statistical decay

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253

Table 3 Hole states of Z°71?b Peak #

Ep,* (MeV)

Jff

1

7.37

1

2

8.10

2

_

2

3

9.00

4

9.96

+ 2 2 27 + 9+ 2

Ex (MeV)

Em (MeV)

0.0

7.368

0.570 0.898

7.938 8.266

1 .633

9.001

2.340 2.623 2.662 2.728

9.708 9.991 10.030 10.096

will populate the same levels . Moreover, the choice of the spin for decaying states at a relatively low excitation energy influences the calculated spectra significantly. To compare the calculations with the data the missing-energy spectra of the four detectors at 0 = 91', 103°, 116° and 129° were summed. Furthermore, the spin was taken to be J'r = 1 - , but the results of calculations using other spin values will be presented as well. Figs . 6a-d show the missing-energy spectra for the four excitation-energy bins between 10.2 < Ex (208Pb) < 15 .4 MeV For each of these four spectra the scaling factor R for the calculated spectra was determined separately by requiring that the data do not overshoot the calculations. It is seen from Fig. 6 that the calculations reproduce the data reasonably well . In Fig. 6e, the sum of the four consecutive spectra are displayed for both the data as well as for the calculations using the scaling factors R determined for the four individual missing-energy spectra. Similar calculations were performed and compared with the data using J'r = 2+ and 4+ as the value for the spin. Fig. 9 shows the results of these calculations . It is seen, that especially the population of the low-spin states below 1 MeV in excitation energy in 207Pb relative to the population of the states at 1.6 MeV (2 +) and around 2.6 MeV ( 2 + to 2 +) in the daughter nucleus (see Table 3) is sensitive to the choice of the spin. Therefore the extraction of the strength for the non-statistical decay of states at an 208 Pb is quite ambiguous. However, for the excitation energy of less than 13 MeV in decay from states at higher excitation energies in 2°8pb it is seen that the choice of the spin has only a minor influence on the results of the calculations. Figs . 6c and d show that the data overshoot the calculations at E,n ;-- 8.5 MeV; i.e. in the region of the hole states in 207Pb (see Table 3) . To study the behaviour of this non-statistical part as a function of the neutron angle, for each neutron detector the (2°8pb) < 15 .4 MeV missing-energy data for the decay from the region 12 .8 < Ex were compared with the calculations . Using the spectra calculated for the J, = 1spin, the non-statistical decay as a function of 0, was determined summed over an energy range from 6 < Em < 11 MeV The results of this analysis are displayed in

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

254

2000

Ex = 11 .5 - 12.8 MeV

1000

2000 4-1

O U

1000 0 1000

Ex = 14.1 - 15 .4 MeV

500 6

8

10

12

14

6

8

10

12

14

E m (MeV) Fig. 9. Missing-energy spectra for the decay from 10.2 < Ex < 15.4 MeV The solid lines indicate the results of statistical model calculations assuming J1r = 2+ (left panel) and J1 = 4+ (right panel).

Fig. 10. 4.2. Decay from the 15 < Ex < 20 MeV region

Fig. 11 shows the missing-energy spectra and their sum for four consecutive excitationenergy bins in the region just above the IVDR resonance. The solid lines in the figure display the calculated statistical decay spectra following the prescription outlined in Sections 3.3 and 4.1 . The spin was taken to be J1 = 1 -. It is seen from Fig. 11 that the population of states at 7 < Em < 11 MeV can be attributed almost completely to

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266 100

E,= 12.8- 15.4MeV

50

255

4 0 0

0 100

E = 15.4 - 20.5 NIeV

50

0 40

r L O U

0 40

0 0 E

x

0

0

0

00

0

= 20.5 - 25 .6 WIeV

"oo+

o "

E = 25.6 - 30.7 MeV

20

10

o

"

0

' "o00

E = 30.7-35.8MeV

j

5 . +

-180

o

l

-90

0

o

90

.o. 180

en (degrees) Fig. 10. Non-statistical yield as a function 2°s of Pb .

of the

neutron angle and for different bins in the excitation energy

non-statistical decay. In contrast to the analysis described in the previous section the value taken for the scaling factor R has only little influence on the determination of the non-statistical part in the missing-energy spectra for Et < 11 MeV To determine the population of the hole states, the four consecutive missing-energy spectra were added for each neutron detector. The angular distribution of the non-statistical decay to the missing-energy region between 7 < Em < 11 MeV is displayed in Fig. 10.

256

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

500

a) E. = 15 .4 - 16.7 MeV

250 0 F-00

b) E. = 16.7 - 17 .9 Me~ 1

250 0 500

M O w

C)

Ex

=

17.9 - 19.2 MeV

250

N +1

0

O U

500

cO E. = 192 - 20.5 MeV

250

e

"...... ..

0

..

e)E.= 15.4-20.5MeV

100(l 500 0

5

10

15

E. (MeV)

20

Fig. 11 . Missing-energy spectra for the decay from 15 .4 < Ex < 20 .5 MeV The solid lines indicate the results of statistical triodel calculations assuming J1 = 1 - for the initial states .

4.3. Decay from the 20 < Ex < 40 MeV region In Fig. 12, the decay spectra for the excitation-energy region between 20.5 and 41 .0 in 2°sPb are displayed. The solid lines in the figure display the results of the statistical model calculations using the parameter sets as described before . To produce the measured and calculated spectra shown in the figure four consecutive missing-energy spectra were added together with, for each calculated spectrum, a separate scaling factor R. It is seen from this figure that with increasing excitation energy in 2°sPb the relative population of the hole states decreases steadily. For the missing-energy range from 7 to 11 MeV, the number of counts as a function of the neutron angle is displayed in Fig. 10 . In

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257

1000 500 0

N N O v

1000 500 0 800 400 0

5

15

25

E m (MeV)

35

45

Fig . 12. Missing-energy spectra for the decay from 20.5 < Ex < 41 .0 MeV The solid lines indicate the results of statistical model calculations assuming JI = 1 - for the initial states .

addition to the hole-state population, Fig. 12a shows evidence for a non-statistical decay component leading to states with Et ;z~ 20 MeV This missing energy corresponds to a final-state energy of about 12 MeV in 207Pb . 4.4. Decay from the 40 < Ex < 60 MeV region The decay spectra for this excitation-energy region can be described almost completely by the results of the statistical model calculations. This is shown in Fig. 13 . The shape of the missing-energy spectra is very well reproduced by the calculations, and the normalization of the calculations to the data changes little as a function of the excitation energy ; see Fig. 8.

258

A.M. van den Berg et al./Nuclear Physics A 578 (1994) 238-266

500 250 0

N CV O N O U

500 250 0 400 200 0 400 200 0

5

15

25

35

45

E m (MeV)

55

65

Fig. 13 . Missing-energy spectra for the decay from 41 .0 < Ex < 61 .4 MeV The solid lines indicate the results of statistical model calculations assuming J1 = 1 - for the initial states.

5. Discussion 5.1. Statistical decay The comparison of the calculations with the data shows that the statistical component in the neutron-decay channel can be described adequately by the calculations over a large excitation-energy region covered by the present study. No need was found to change the parameter set listed in Table 2 which was determined from a phenomenological description of other data sets. This holds both for the parameters used at low excitation energies given by and interpolated from the values listed in Ref. [41 ] and for the leveldensity parameters from the liquid-drop model [ 43 ] . Especially, for an excitation energy in 2°8Pb higher than 45 MeV the calculated spectra agree very well with the data and the scaling factor R is almost constant in this energy region (see Fig. 8) . In the present

A.M. van den Berg et al./Nuclear Physics A 578 (1994) 238-266

259

experiment the excitation energy in the entry channel of the compound nucleus is known very well, and this agreement gives confidence in the statistical model calculations using standard parameters .

At excitation energies below 40 MeV in 2°8Pb two things happen. Firstly, in addition

to the pure statistical decay component there is evidently non-statistical decay. Tlu; importance of the non-statistical decay component leading to the bole states in 207Pb increases rapidly with decreasing excitation energy in 2°gPb (see Figs. 11 at., . 12). This

will be discussed in more detail in Section 5.2 . Secondly, the scaling factor R used to normalize the calculations to the data increases with decreasing excitation energy ; see Fig. 8. This effect is not understood. As it is plausible that at a high excitation energy

the decay is purely statistical, the calculations predict a too small neutron multiplicity

at low excitation energy and/or a too large multiplicity at high excitation energy. But even large changes of the parameters used in the statistical model calculations influence

the curve shown in Fig. 8 little. Another possible explanation can be that the singles spectrum has an unidentified component. This could be a contribution from a reaction

process other than inelastic scattering which does not emit neutrons in the angular region covered in this experiment, such as the pick-up-break-up process, or it could be an

instrumental background component which is reiatively more important at high excitation

energies than at small excitation energies . But, although an instrumental background has been identified in the present experiment (see Section 3.1) and for which the downscaled singles spectrum has been corrected, there is no evidence for other sources of instrumental background . 5.2. Non-statistical decay to hole states The decay strength to hole states in the residual nucleus, remaining after subtraction of the calculated statistical contribution, is interpreted as being due to direct and

pre-equilibrium decay. These two decay mechanisms can be distinguished when the corresponding excitation energies are different in the final nucleus.

Although statistical decay clearly dominates at all excitation energies, there is also

a definite non-statistical contribution up to excitation energies as high as 30 MeV For 2°7Pb E.,(2°8Pb) < 22 MeV most of this non-statistical part populates the hole-states in which are located in the range 7.4 < Em < 11 MeV It is seen from Fig. 11 that for 208Pb the the decay from the excitation-energy region between 15 .4 and 20 .5 MeV in

component of the non-statistical decay process is very little influenced by the results of the statistical model calculations . The non-statistical component of the missing-energy

spectra was fitted with four Gaussian shaped peaks while keeping the position and

the width of each peak fixed. Both the time resolution in the neutron time-of-flight 170 ions determine the width of measurement and the energy resolution of the detected these Gaussian-shaped peaks. Using the numbers quoted in Section 2 the width of the peaks was calculated to be 1 .2 MeV (FWHM) . The hole states were treated as four different peaks centered at the positions Epeak (see Table 3) . The extracted number of

counts for each peak normalized with the factor W~e1 is shown in Fig. 14 . It is seen that

260

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266 40

a)

20 0 40 a)

4-

0 U

b)

20

40

c)

20

40

d)

20

"

O -180

-90

0

90

180

on (degrees) Fig. 14. Hole-state population for tfie non-statistical decay to four different peaks centered at an excitation energy of 0.0, 0.73, 1 .63 and 2.59 MeV (panels a, b, c and d, respectively) in 2°7Pb as a function of the neutron angle.

for all four groups the general behaviour which is displayed in Fig. 10 persists, be it that the population of the lowest lying levels shows a more pronounced angular pattern than that of the higher lying levels . In order to see whether this behaviour is related to the scattering angle of the 170 particles coincident events with small and large scattering angles were treated separately. Therefore one software window on the scattering angle was used in the angular range between 1 .5° < Olab < 2.5° and another one in the angular range between 2.5° < Olab < 4.5°. For both angular intervals the hole-state population in the missing-energy range from 6 < Em < 11 MeV was determined for the detectors positioned between neutron angles Bn = 78° and 103 ° . The number of counts weighted with the factor Wrel for the hole-state population is shown in Fig. 15 . Also in this figure a systematic angular behaviour of the hole-state population can be recognized . For the large-angle scattering (i.e. 2.5° < Blab < 4.5°) the population of the hole states shows a more or less isotropic distribution, and the number of counts decreases gradually with increasing

A .M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

26 1

10 5 0

15

20

25

Ex (MeV)

30

35

Fig. 15. Population of hole-states with 6 < Em < 11 MeV as a function of the excitation energy for two different bins of the scattering angle of "0. excitation energy in 2°8Pb. At the same time, however, the data analysed

for the small-

angle scattering window (i .e . 1 .5 ° < elab < 2.5°) shows a behaviou . that resembles very much the trends recognized in Fig. 10 ; the renormalized number of counts increases

with decreasing neutron angles 0, As stated before it should be noted that the factor

W, e1 accounts only for the relative detection efficiency of the different neutron detectors for a specified (range of the) neutron energy. This implies that Figs . 10 and 15 cannot

be used directly to determine the actual relative yield for low- and high-energy neutrons . However, the trends shown in these two figures will remain if such corrections

for the

energy-dependent efficiency are applied.

Various processes are known to contribute to the population of hole states (see among others Ref. [21]) . In addition to the direct decay of excited states there is the process of knock-out which interferes with the direct-decay process and causes a foreaft asymmetry along the recoil direction . The amplitude of the knock-out contribution is much larger at forward than at backward angles, with respect to the recoil direction. If this process is important one expects that the relative population of the hole states

in the recoil direction should be much larger than in the anti-recoil one. Fig. 10 shows that this is not the case for the system studied here. We conclude that in small-angle inelastic scattering of 170 at 1428 MeV the contribution from the knock-out process is

262

A.M. van den Berg et al. /Nuclear Physics A 578 (1994) 238-266

small if not negligibly: in the phase space covered by the present experiment. This is quite different from what is found in inelastic a-scattering [9,11-13] . The measured distributions shown in Figs. 10 and 15 indicate that our understanding of the decay and/or excitation process of 1p-lh states in the continuum is incomplete. Naivety the angular distribution for the decay neutrons is expected to be symmetric with respect to the recoil angle (9 ;z:; 80° at Ex = 20 MeV; see Fig. 2) . This is evidently not the case, if the 170 particles are scattered into the angular range between 1 .5° < Blab < 2.5°. At the same time, however, for larger scattering angles the angular correlations tend to be more isotropic, and symmetry with respect to the recoil angle cannot be excluded . Whether the angular correlations can be explained by one and the same process or if at least two different processes are required remains unclear. Analysis of the angular-correlation pattern as well as the hole-state population (see Fig. 14) suggest that there are two different processes feeding the hole states : the direct decay of excited structures, probably consisting of overlapping, broad giant resonances having an angular-correlation pattern approximately symmetric around an angle close to the recoil and anti-recoil direction, and another process, strongly populating the lowlying hole states and having a more forward-peaked angular-correlation pattern. The phenomena shown in Fig. 10 are also found in the study of the same reaction using a 124Sn target, but less pronounced than in the present case, whereas in the study of the excitation and decay of 9°Zr no evidence was found for these phenomena (see paper H) . Similar angular correlations have been observed earlier by Okada et al. [461 who studied the neutron decay of 119Sn nuclei excited by a-particles at a bombarding energy of 27 MeV/nucleon. 5.3. Non-statistical decay to other states It is seen from Fig. 12 that in addition to the non-statistical decay to the hole states in 2°7Pb states there is also non-statistical decay to other states as well. For instance, in the decay from the region between 20.5 and 25.6 MeV in 2°8Pb states are populated

at a missing energy between 11 and 14 MeV and around 20 MeV, which cannot be described by the statistical model calculations . In the first region with 11 < E,n < 14 MeV there is a group of lp-2h states in 2°7Pb . In a weak-coupling model these can be described as the coupling of the collective J' = 3- in 208Pb at Ex = 2.61 MeV to the neutron hole states in 207 Pb. Therefore this non-statistical decay component can be explained partially as pre-equilibrium decay in a way similar to the analysis given by Brandenburg et al. [9] . The decay spectra for the excitation-energy region from 20 < Ex (2°sPb) < 25 MeV also show a non-statistical decay component (see Fig. 12a) . In addition to this, the scaling factor R for this excitation-energy region appears to be larger as expected on basis of an interpolation from the neighbouring regions. Both effects point to the hypothesis that there is an enhanced decay from a structure at an excitation energy of about 25 MeV in 2°spb to a structure at a missing energy of about 20 MeV, e.g. 12 MeV in 207Pb. Several states are predicted to lie in the 20-30 MeV excitation energy region of 2°spb,

A.M. van den Berg et al./NuclearPhysics A 578 (1994) 238-266

263

among them double-phonon states built either with the IVDR or the ISQR, and also the isovector giant quadrupole resonance (IVQR) . Recently evidence has been given for excitation through Coulomb interaction of the double lVDR in relativistic heavyion collisions (E " 1 GeV/nucleon) using very heavy projectiles [47,48] . However, in the present case, due to the much lower beam energy and lighter projectile, the times Coulomb excitation of the double IVDR is expected to be very small, about 1 less than the single IVDR [49], and should be undetectable. On the other hand, the double ISQR, excited mainly by the nuclear interaction, has been observed in the 4°Ca + 4°Ca reaction at 50 MeV/nucleon, with a cross section only about a factor of 10 less than the single ISQR [ 19] . It was observed to decay through the single ISQR of the (A - 1) nucleus, which resembles the decay pattern observed here. Thus, the double ISQR could contribute to the observed structure. Another contribution to the observed structure could be the IVQR. Evidence for this resonance has been found by Drake et al. [50], and recently by Dale et al. [51], who located the centroid of the resonance at an excitation energy of 20 MeV Also other data support the existence of this resonance at this excitation energy (see among others Ref. [52J) ; the increase of the scaling factor in this excitation-energy region and the decay seen in the present experiment at Em = 20 MeV may also contain contributions from the decay of the IVQR to the IVDR. However, the present data provide no evidence to support these hypotheses.

6. Summary and conclusions In the present experiment neutron decay from the excitation-energy region 10 to 60 MeV in 2°8Pb, i.e. from the giant resonance region to far above, has been studied . 170 ions of 84 MeV/nucleon The 208Pb nucleus was excited by inelastic scattering of at scattering angles 1 .5° -- elab < 4.5°, a set of conditions for which it is known [23,34] that giant resonances are strongly excited. Most of the neutron detectors were arranged around the anti-recoil direction where one expects that direct decay from 124Sn are particle-unstp_bie excited states can be observed. Similar data on 9°Zr and published ; n paper (H) . The statistical decay component was found to be the dominant one for excitation energies larger than 13 MeV; for lower excitation energies the statistical and nonstatistical contributions cannot be disentangled. The shape of the missing-energy spectra can be described by statistical model calculations with standard parameters [9] . Non-statistical decay, although small, is clearly present up to excitation energies of about 30 MeV The direct decay branch decreases from around 16 MeV to a very small value at 25 MeV and above. In addition to a direct part populating hole states in the residual nucleus 2°7Pb, there is evidence for some non-statistical decay to other than hole states which suggests a pre-equilibrium process . The knock-out contribution which should manifest itself in the recoil direction, is small. This is quite different for inelastic a-scattering at 30 MeV/nucleon [9,12,131 . There is evidence that, in addition to direct decay of excited structures, there is

266

[351 [361 [371 [381 [ 391 [401 [411 [421 [411 [441 [451 [461

[471

[481

[491 501 [511 1521 [531

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r