The Munich RF-recoil spectrometer for the observation of heavy-ion reaction products at zero degree

Nuclear Instruments and Methods 204 (1983) 407-418 North-Holland Publishing Company

THE MUNICH RF-RECOIL SPECTROMETER REACTION PRODUCTS AT ZERO DEGREE

407

FOR THE OBSERVATION

K. R U D O L P H , D . E V E R S , P. K O N R A D , K . E . G . L O B N E R , S.J. S K O R K A a n d I. W E I D L University of Munich, 8046 Garching, Fed. Rep. Germany

OF HEAVY-ION

U. QUADE,

Received 29 April 1982

The design and performance of a new type of heavy-ion recoil spectrometer is described. The instrument allows the separation and identification of reaction products at 0 ° and consists of a high transmission crossed field radio-frequency velocity filter, a time of flight detector and a large window ionization chamber. The device can be applied in investigations of heavy nuclei recoiling from targets in fusion, transfer or fission processes. Coincidence experiments of the recoils with evaporated light particles, back-scattered projectile-like heavy ions or prompt gamma rays are possible.

1. Introduction

In a heavy-ion fusion reaction the fusion products (evaporation residues) recoil from the target within a narrow cone around zero degree and hence are partly embedded in the projectile beam. In the extreme case of heavy-ion radiative capture typically 80% of the recoils travel within 15 mrad of the beam direction. The kinematic angular spread of evaporation residues of (heavy ion, xn)-reactions is somewhat larger; however, their efficient detection outside the main projectile beam can still suffer considerably from the multiply and Rutherford scattered projectiles. The differential cross section in the laboratory system is largest at zero degree. In order to be able to detect the recoil nuclei at 0 °, recoil spectrometers have been developed at several laboratories [ 1-3]. Similar instruments are being planned at other places. A review article has recently been published by Enge [4]. The recoil spectrometer described below was designed in 1973 [5] and has been used for several years in the search for heavy-ion radiative capture [6], for the investigation of the decay modes of unbound high spin states [7], and for measurements of subbarrier fusion cross sections [8]. The device (fig. 1) consists of a velocity selector (Wien filter) and a heavy-ion detector system. A unique feature of the velocity filter, which suppresses the bulk of the projectiles but permits the passage of the reaction products, is the use of radio frequency instead of dc voltage for the electric deflection. The magnetic field is constant in time. The detector system consists of a time detector for the determination of the recoil velocity v and a multiparameter ioni0167-5087/83/0000-0000/$03.00 © 1983 North-Holland

zation chamber, which is used to measure the particle energy E and hence, together with v, the mass number A of the particle. Also, the energy loss AE, and hence the nuclear charge number Z, is measured. The chamber is capable of position identification in the plane perpendicular to the beam. A lens is used to focus the reaction products into the detector system. Pulsing of

Table 1 Specifications of the Munich recoil spectrometer Configuration Maximum solid angle Maximum acceptance angle Focal plane magnification Velocity window (typically) Charge window (typically) Maximum electric rigidity Maximum magnetic rigidity a) Integral suppression (typically) Velocity resolution Energy resolution Mass resolution Transmission b) (typically) Detection efficiency b) (typically) Isochronism Total length target detector

2QDED (or 3QDED) 3 msr 32 mrad --4 15-20% 30% 25 MV 800 MV ns/m =0.8 T m 10 s A v / v = (0.15-0.5) f E / A % ~ E / E ~--0.6-1.5% A m / m ~--1-2% 40% 20% A t / t ~-- 1.5 X 10-3 --4 m

a) Limited by quadrupoles. b) Neutron evaporation residues, medium weight nuclei, including transmission through grid supported entrance window of detector.

408

K. Rudolph et al. / The Munich rf-recoil spectrometer

the projectile beam is required both for the optimum performance of the rf-Wien filter and the time of flight measurement of the particles. Due to the recent development of high efficiency bunchers [9] the requirement of pulsing does not result in a serious reduction in beam intensity. Some features of the spectrometer are listed in table 1. In the following section the underlying general considerations for the design of the recoil spectrometer are discussed. In section 3 the performance characteristics of the rf-separator are explained and its main properties are derived. Section 4 gives a description of the detector system used for the particle identification, and in section 5 the acceptance, transmission, and efficiency of the device as a whole are considered. In a final section (6) the operation experience and the calibration procedures are discussed.

2. Basic design considerations In many heavy-ion reactions the intensity of a particular reaction channel of interest is very low. The measurements mentioned above are typical examples of low counting-rate experiments. Therefore, a large solid angle and a high transmission are desirable properties of a good heavy-ion recoil spectrometer. Other important features are a high mass resolution and a sufficiently large suppression of the beam particles. To approach these partly conflicting requisites two different methods can be employed. One of them is the use of large electric and magnetic fields with good optical properties in combination with focusing and correction elements in order to transport selected recoils to a focal plane. Such devices offer mass resolving powers as large as 500 and more, together with solid angles of several msr. Aside from having a high mass dispersion they focus the particles independently of direction and energy. Spectrometers of this kind are being constructed in Osaka [10] and Rochester [11]. They require a large space and considerable investments of manpower and money. In general their transmission is restricted to one charge state. This is a severe limitation to the counting efficiency. The second possibility of constructing a recoil spectrometer is to employ electromagnetic fields exclusively in order to suppress the projectile beam. In this case the total cost, manpower expenditure, and space requirement at a given total detection efficiency is relatively low. Velocity and mass of the recoils of interest are measured with the help of proper nuclear detectors and electronics. Limited by the state of the art of particle energy determination, the mass resolving power is in this case restricted to about 50 to 100, depending on the mass number and energy. The system has no mass dispersion in the recoil mass region.

The Munich recoil spectrometer is of the latter kind. The highly isochronous beam transport through the separator facilitates the velocity determination by time of flight, allowing a velocity resolving power of 5001500. A large solid angle and high transmission are possible and the accepted velocity range is large. The velocity window approximately matches the velocity spread of evaporation residues, which is typically 10 to 20%. In the case of a-evaporation residues this matching is possible only for favourable recoil momentum ratios. The zero total deflection of the recoils basically allows an atomic charge independent transport of the particles through the system and hence a large charge window. The addition of focusing elements conflicts with the desire for a complete charge independence but is necessary for a large angular acceptance. To accommodate a large phase space of the recoil nuclei and a large charge window in spite of the limited charge independence of the focusing element, all apertures and gaps must be sufficiently wide and the total length of the spectrometer must be as short as possible. In particular, the time detector and the ionization chamber must be large area devices. With regard to the very high intensity of the projectiles relative to the reaction products, a large suppression factor is essential. In order to avoid pile-up effects in the detector system, the counting rate must be limited to about 104/s or less. Assuming 1011-1012 projectiles/s, the integral suppression factor should be larger than 10 7 - 1 0 8 . The sensitivity of the spectrometer (minimum detectable cross section) depends on the intensity of scattered background particles falsely registered with apparent mass, energy, velocity, and energy loss of the recoil nuclei of interest, and is determined by the time and energy resolutions of the detection system and the pulse width of the projectile beam as well as by strength and shape of the suppressing fields and the details of the mechanical structure of the system. High projectile suppression factors can be achieved by the redundant combination of several filters in series. Such a design, however, is in conflict with the demand for a large charge window, a large velocity window and a high transmission at a large solid angle. Experience shows that an integral suppression as high as 108 and more is possible with a one-stage system, if the separation angle between recoils and projectiles is sufficiently large. Since the projectiles in a typical fusion reaction (not too far above the Coulomb barrier) have approximately the same magnetic rigidity as the reaction products, but only half the electric rigidity, electric deflection must be at least partly employed. The separator of the Munich recoil spectrometer (fig. 1) consists of an electric deflector combined with two dipole magnets symmetrically arranged in front of and behind the electric deflector. The system acts as a separate-function velocity selector. The deflector plates

409

K. Rudolph et a L / The Munich rf-recoil spectrometer Beam Filter Lens _

,

larlget

~

IB~

Time pickup

"~" Ee ~

___L:

Recois

Beam

.. i

~nization Chamber

70

AT=A r

. i

~o=21~ ~os =T~/6

60 ,

v s

Projectiles

,'pla0

A

Fig. 1. Schematic view of the Munich recoil spectrometer. The reaction products (recoils) are focused to the detector system and separated from the projectiles. Recoil identification is performed by flight time, energy and energy loss measurements.

50

Reioil Window

,

40

Pr°jeitile Beam

3+

3O

i /< ,i0 +

20

~ r f - F i l t e r F i l -t e r z

10 0 -10

are as short as 25 cm with a large plate distance of 7.0 cm. Together with the very short dipoles (effective length 17cm, pole distance 10cm) they represent a compact arrangement with a corresponding low probability of projectile scattering. Beyond that, the deflection plates are mounted asymmetrically with respect to the optical axis to minimize deflected particles hitting the deflector plate. Considering the limitations of the electric field strength applicable in vacuum and the requirements of the compact geometry, the use of rf-deflection offers important advantages in comparison to dc-voltage. The rf-velocity filter combined with the use of a pulsed projectile beam allows particles to pass only within limited velocity windows and limited time windows. As a result of this additional restriction and particularly due to the change in sign of the electric field, the deflection angle on both sides of the velocity window and especially for all velocities above the recoil velocity is considerably increased. This is illustrated in figs. 2 and 3 and will be explained in more detail in the next section. Moreover, the "quadratic" dependence of the deflection angle within the velocity window meets the requirement of a large window size at a given projectile separation angle. Within large parts of the velocity window the velocity dispersion is small. The control and stabilization of rf-amplitudes and phases is electronically possible with high precision and reliability. As a consequence of the time dependence of the filter, the target-to-filter distance L a n d / o r the deflection frequency w must be roughly matched to the projectile-recoil velocity difference for optimum separation. This requirement is not critical at all, as will be explained in the next section. The reliable determination of the detection efficiency of the system is very much simplified by the straight geometry, which allows a precise alignment of all mechanical components.

/

-20

I"

I/

-30

/

/

/ ] / I

-A0 -50

~]7%

\Itl t

/

!

Anglar Accept. . . .

LI-3

t.~x

of Detector System

'

~R

19+

, ./ ~./

[2 .0~{ . /(XR(dC) it / //~/ I /

\.~. "~ I J.'> ~,... ~..,,.~ i

o.96~-~'% t.o~v/v.'O,

// / /

I

"l

I_ I

-2

Fig. 2. Deflection angle as a function of relative velocity. The assumed charge states correspond to the most abundant (equilibration) charge at the respective velocity. The assumed reaction is 4°Ca+4°Ca at a laboratory energy of E L = 100 MeV. For a typical electric field strength of 1.8 MV/m, s 0--5.8 mrad. For the definition of the constants ~ and £0, see fig. 3 and text (formulae (15) and (16)). The charge states 8 + to 16 + indicated along the curve are the most probable charge states, and these have been used to calculate the deflection. Ee(t)= Eosin (~t+5)

a)

T 6/

recoils arrive at deflector

/

t:lO, ~ i-articles leave target

t~o~ \ i -t

{ ~ ~/w i i

Projectiles arrlve at deflector b)

(

s

)

I

I" Target

L

,II deflector plates

Fig. 3. Explanation of notation used in the text. E~(t)=electric field strength as a function of time.

K. Rudolph et al. / The Munich rf-recoil spectrometer

410

3. The if-velocity filter

must be fulfilled. The two conditions (8) and (9) define the rf-phase and the field settings of the Wien filter

In this section the essential parts of the formalism of the rf-velocity filter are presented and some properties are derived. It is practical to introduce the abbreviation

Bsm __ F a ' ( v ~ ' )

-/=

and result in the deflection function for the recoils of interest

,

=0.0139m/(ns.

Mv/-MeV)

(1)

}/moc2

E 0s

(10)

v~)

ag(VFt) = aoqRZ(VR/V~ )) with mo c2= 931.5 MeV, and to measure electric voltages in MV and magnetic fields B in MV n s / m 2 (--~ 10 Gauss). The electric and magnetic rigidities of a particle of energy E (MeV), mass number A and charge q (in units of the electronic charge e) then are

S o = q2 e

[MV]

and

Sm _- 2 A ~ [ M V

ns/m]

(2)

and its velocity

With the additional conventions of defining the time zero t = 0 when the projectiles arrive at the target and defining the sign of the deflection angle a > 0 for positively charged particles in the magnetic field, one has, with a few reasonable approximations for the magnetic deflection

Bsm

(12)

Here the projectiles are assumed to carry the constant velocity Vp from the target to the separator and to start at t = 0 at the target. Projectiles with different histories are discussed below. In eqs. (11) and (12) the abbreviation F I 10)

E°s T k v ~ ~ a0

(tad per charge state)

(13)

2E~)

is used. where E ~ ) denotes the recoil energy in the laboratory system. AR is the recoil mass number (before particle evaporation) and Ap refers to the mass number of projectiles. The function z ( x ) is defined by

(4)

~ m - - Sm

and contains the two phase constants

and for the electric deflection

t..OS

~.~- 2 v ~ ) Ore--

)).

O~p(Vp) = a0q p ~ z ( v p / v ~

(3)

v = yv/E/A •

(11)

and

E°s FT(V ) sin(wt a + 8).

qo = v~ )

oat~ ).

(16)

(5)

Se

Here s m and s are the effective lengths of the fields; F v ( v ) is the transit time factor for particles of velocity 2v.

coL ----

and

c0s

(6)

r ~ ( v ) = ,os sin 2~

and the electric field is written as (fig. 3)

Eo(t) = E0 sin(o. + 8)

o a - A t = ( 2 m + 1) rr

(7)

with 0~<6<2~r. The rf-frequency is described by oa(ns-1), and t, is the time of arrival of the particle at the center of the deflection plates (t a = L / v ) . Denoting the velocity of the standard recoil particle of interest by v~ ) its arrival time is t~ ) = L / v ~ ). The velocity window is positioned at v~ ) by the condition

(8)

a(v~)) = 0

They depend on the parameters ~0 and L. While % determines the transit time effect, q~ is available for the optimization of the separation of the standard pro(0) jectiles with the beam velocity Vp _- . Vp . If At = t~ ~- - t-p(°) is the difference of the flight times of standard recoils and standard projectiles, the best choice for optimum separation is (m=0,

1,2 ...).

(17)

Neglecting target energy losses and considering the particular case of fusion (%(0)~4p = v~)AR) it is, on the other hand,

At -

L AT v~) A R

(18)

and hence,

wL = (2m + 1)

~'~R(0)AR•

(19)

AT

(with a = a m q-ae). The field strength ratio is fixed in this manner. In addition, for approximate zero velocity dispersion near the center of the velocity window (and more generally than indicated in fig. 3) the condition

wt~)+6=(4n+l)2

,

n=l,2

...

(9)

Here A T = A R -Ap denotes the target mass number. Fig. 4 displays optimum target-deflector distances L for fusion reactions near the Coulomb barrier and for frequencies 2.5, 5 and 10 MHz. A variation of L can be accomplished by moving the components of the separa-

411

K. Rudolph et al. / The Munich rf-recoil spectrometer

2.5 Lira ) 2.0

xx,,x

1.5 1.0 0.5 5;

I

I

I

I AT+Ap I

100

150

2;0

Fig. 4. Optimum target-deflector distance for fusion reactions as a function of mass number. L~<1.2 m is excluded due to space requirements of the lens and other components. As explained in the text, moderate deviations from the optimum L do not appreciably affect the separation angle. Parameter: frequency ~0 of rf-deflector.

phasized that the great majority of the projectiles leaving the target have the velocity Vp = -Vp(0). in this particular example t~p -(0)/,,(0)_ / ~ R -- 2. However, experience shows that the appearance of projectile particles with vp < v(p°) is quite common jn practice. Depending on their origin most of the projectiles leaking through the velocity window have an energy which is, in the selected example, only one-half of that of the recoils. They are easily discriminated by the detection system. At very low projectile velocities the rf-filter exhibits a large number of very narrow additional windows. However, the total width of these windows amounts to only a few percent, and the corresponding energy is very low. They do not give rise to any difficulty. Fig. 2 indicates that the center of the velocity window of the rf-filter is, in fact, somewhat lower than v(R °), a small effect of no practical importance. The relative width A v / v ~ ) of the velocity window for a particle of charge state q can be estimated to be Av _ 2 , / 2xa

tor on precision rails without losing the alignment. The conversion of the separator to another frequency requires replacing the rf-coil of the deflector circuit and making minor changes in the driver unit. Of course, must be an integer multiple of the repetition frequency of the pulsed beam. If, for practical reasons, the optim u m choice of L cannot be employed, the phase between recoils and projectiles will deviate from ,r. Denoting the deviation by xI, (fig. 3) one now has ~ o L = v ~ ) ~ = [ ( 2 m + 1) ~r -t- ~ ]

v~)AR/AT

(20)

with - - T r ~ < f f ' ~ r . As far as the separation angle is concerned, the extreme choice of if' = ±~r corresponds to some extent to the dc-velocity filter. Neglecting for the following comparisons the transit time effects (% -0), which are, indeed, in most applications of minor importance, one can show the deflection angle of the standard projectile ( % = v~p°)) to be (again fusion reaction assumed)

V(R °)

(23)

q~ V a°q

In accordance with the quadratic behaviour of the particle deflection near v~ ) this width depends on the square root of the angular acceptance Aa of the detector system. For a broad velocity window the parameter cp = ~ o L / v ~ ) should be small, i.e. m = 0 whenever possible (see formula (19)). Typically, one has Aa --~ 20 mrad and A v / v ~ ) ~-- 15%. It should be considered, of course, that the charge distribution and the finite phase space of the recoils (and projectiles) complicate the picture given by fig. 2. A quantitative discussion of the transmission through the velocity window is given in section 5.

5C - ap/~ 0

- ....

II

e=2r~ % = re/6 AT=Ap

z.0-

O/p( I);O))

l+

cos,.,

.

(21)

The low sensitivity of ap(V(p°1) with respect to q" confirms that even in unfavourable target-projectile combinations the choice of L (or ~o) is not very critical, and that excitation functions can be measured without changing geometry or frequency. The ratio co) ~,]*=oo Otp[~ L~p

-- 1 + 2~-~T indicates the superiority of the rf-separator to the version, especially for large Ap/,Zl T. In fig. 2 the functions aR(VR) and ot_(Vp) are played for a case A p - - A T , e.g. 4 ° c a + a ~ c a , with parameters cp= 2*r and % = 27r/12. It should be

['~ 3C20-

(22) dcdisthe em-

!/,

?

1(3-

anaular (~CeDIQ~

Ap

LdL= 0.25 LtlL =_2. 5

-I0

\

i Vp ]VR(OI - -

I0"

delect~

Fig. 5. Deflection angle of projectile particles of relative velocity v p /-.~ C0) R scattere d by obstacles (e.g. slit edges) at distance Lj from the target. Their apparent velocity determined by the time signal of the time detector differs from their actual velocity %. Their discrimination against the recoils under investigation is generally possible via E and AE measurement.

412

K. Rudolph et al. / The Munich rf-recoil spectrometer

A contribution to the background can be produced by particles being scattered from beam apertures far in front of the target or between target and separator, especially from the acceptance aperture of the spectrometer. This aperture is placed at the entrance of the lens. Fig. 5 shows two examples of deflection functions. It is assumed that the particles change velocity from V(p°) to Vp at a position L 1 behind the target. The entrance aperture is placed at about L x / L = 0 . 2 5 . The corresponding background particles carry energies of less than one-half of the recoils. Obstacles in front of the target (L1 < 0) can be more critical. Again the redundant determination of the velocity, the energy loss, and the energy by the detector system allows a discrimination of the recoils of interest against these scattered projectiles.

4. The detector system The flight time of the recoils is measured as the time difference of a start pulse from the time detector and a stop pulse derived from the beam pulsing system. The time detector consists of two grid-supported carbon foils (10-15 # g / c m 2) inclined at ± 45 ° with respect to the beam axis (fig. 6). A similar arrangement has been employed by Kohlmeyer et al. [12]. Secondary electrons are accelerated by 1.5 kV and detected with the help of two pairs of channel plates, each connected in series with a total amplification of 106. The time errors resulting from the inclination of the two carbon foils have opposite signs. The corrected flight time (t I + t 2 ) / 2 can be determined by an electronic time compensator or calculated by the on-line program. The resulting detector time resolution for 80 MeV 32S is about 200 ps to be compared with the beam pulse width of 300 to 500 ps (with the recently installed post acceleration buncher

Position Y

O K V - ~ SeiS)~XlSt -r~/

,,

-3.0KV. . . . ~/ -4.SKV- "

// Anode

~

~ Eres

Fig. 7. Principle construction of the ionization chamber.

~Frlsch

...............,

•

-

Anode ,,,'---,"N)'~" ~4~r°nelPlates

~,)---/-/ AccelerationGrid ~ - CarbonFoil, supported

[13]) or approximately 1 ns (using the standard bunching system). The flight path target-detector is about 3 m, the relative error of the velocity measurement typically amounts to about 0.3%. Other important features of the time detector are its large effective diameter of 50 mm in the direction of the inclination and 70 mm in the other direction, its detection efficiency for heavy ions, (normally 95 ± 5%) and its transmission due to the transparency of the grids (86%). The multiparameter ionization chamber [14] is provided with an entrance window of 64 mm diameter and is 21.0 cm long. The window consists of a 50 # g / c m 2 polypropylene foil supported by a stainless steel grid with 81% transmission. The counting gas is methane (99.95%) at a typical pressure of 100 mbar and a flow rate of about 100 m g / m i n CH 4. The design of the chamber is shown in fig. 7. The anode plate is subdivided to allow energy loss and residual energy measurements. An additional subdivision of the rear part of the cathode in 8 stripes provides information on the horizontal (x) position while the front part permits the determination of the vertical ( y ) position by a measurement of the electron drift time from the ionization path of the particle to the Frisch-grid, observed as time difference of pulses at the cathode and anode [15].

~&z / /

N:

-

Fig. 6. The micro-channel plate time detector. Channel plates: Type CHEVRON 3075-B-00M00.

Preamplifier

'

~

Grid ~-~*- Z

K. Rudolph et al. / The Munich rf-recoil spectrometer Since first priority has been given to a good energy resolution, the position determination has been achieved by using signals induced by the positive charge carriers. Other methods of position detection impair the energy resolution either by additional grids in the flight path of the primary electrons or even more so, by the amplification of a part of these electrons to be collected for the energy signal. In order to maintain the energy resolution two disadvantages of the position determination have been accepted: (a) The position resolution a d in x depends on the y position of the incoming particle and worsens as the distance from the cathode increases (for 100 MeV 32S ions A d = 1 m m at 1 cm from the cathode and Ad = 5 m m at 7 cm from the cathode); (b) since the electric field is not quite homogenous in the given geometry (due to the very large entrance window), the scale of the x position varies somewhat with the y position. In the present application of the ionization chamber these limitations are small enough to be of no practical importance; if they were considerably important, corrections could be employed. With an energy loss of about 60% in the AE section, a nuclear charge resolving power Z / A Z of about 39 is achieved for fission fragments of 93 MeV [16]. At energies much below 1 M e V / u the Z determination by energy loss measurements becomes increasingly difficult. Fig. 8 shows a Z spectrum obtained during an investigation [7] of the decay modes of high-spin states in 27A1. The recoils from the reaction 160 on 12C have energies close to 1 M e V / u , the Z resolving power is 32-50. The relative energy resolution depends on the energy-loss straggling and inhomogeneity of the entrance window as well as on the collection efficiency determined by the gas and the chamber geometry. If the particle beam is confined to the central part of the entrance window and if the A E and Er~~ plates are connected, an energy resolution of 6 E / E = 0.7% for

413

xl03

ts0 on ~2C

z..O-

EL=53.6MeV

3.2~ 2./.O

1.6-

0.B20

22

24

26 MASSNUMBER Fig. 9. Mass spectrum of Z = 12 recoils from the reaction 160 on 12C. The Mg isotopes 23Mg to 26Mg are identified. The mass resolution is about 55.

2 M e V / u particles of A = 24 can be routinely achieved. The electronic addition of the A E and Er~s signals deteriorates the resolution to 0.9%. A further increase of 6 E / E is caused by the foil inhomogeneity. A central part of the foil of about 2 - 3 cm diameter is very homogenous. If the full window size of 6.4 cm diameter is exposed to the particles, an energy resolution of up to 1.4% is obtained for the case mentioned above. The mass resolving power determined by the flight time and energy measurement is expected to be m / A m = 30-100. Fig. 9 shows an example of a mass spectrum derived from a window on Z -- 12 of the events of fig. 8. The resolving power is about 55, and is in this case equally affected by both the energy and the time resolutions. In recent sub-barrier fusion measurement (ref. 8) the recoils of masses around A --~ 135 carried specific energies of as low as 0.2 M e V / u and the resulting mass resolving power was approximately 32, completely determined by the energy resolution.

5. Counting efficiency and calibration ,10 t 160 on 12C

4.0

E L : 53.6MeV

3.2 z (J

2.4

The transport of the reaction products to the detector is not only influenced by the focusing and deflecting fields but also by a number of apertures and slits, the most important of them being the entrance (acceptance) aperture. The fraction a(Sl) of recoils accepted by this (circular) aperture is given by

0.8 I0

]5 Nuclear Charge Number Z

Fig. 8. Z spectrum of recoils from the reaction 160+ 12C at an energy E L =53.6 MeV in the laboratory system. Specific recoil energies around 1 MeV/u. Nuclear charge resolving power Z/A Z = 32-50.

=

a(O1)

f0

° ~ ( d o / d ~ ) L sin 0 dO ~ f0 ( d o / d ~ ) L sin 0 d0

(24)

and depends on the angular radius OI of the iris aperture and on the differential cross section (in the laboratory system) of the nuclear reaction in question. Since the

K. Rudolph et al. / The Munich rf-recoilspectrometer

414 Fracti on a (1~i) of recoiEs accepted

particle parameters 0, q~, q ... etc. The cross section o R for the production of a certain species of interest then is

'

8Cr)~' /EL(32S)= 85MeV///O/o I

o.~ 0.6

o.< 0.2 /

/

r/

/

/

/

/

/

1

/

,Ndlxn ELI32S)= 115MeV

~OOl--x

oR

~nl ~

, ~Imaxl

r 207

(~),

\ .... \

\

20

,o~R.... s o

30 AO 50 60 70 80 Radius of acceptance aperture (rnrad)

90

~

at

Fig. 10. Fraction of recoils accepted by an entrance aperture of angular radius 01, obtained with a Monte Carlo calculation of the angular distribution of two different recoiling reaction products. Insert: calculated relative differential cross section in the laboratory system of evaporation residues, assuming isotropic neutron evaporation only. acceptance aperture is positioned in front of the first quadrupole, the acceptance a(O 0 is independent of the charge distribution of the recoils. The entrance aperture limits the size of the projectile beam expanded by Rutherford and multiple scattering. A large entrance angle 01 requires large field gaps and large deflection angles, that is, large field strengths. Probably the cost of the spectrometer increases at least quadratically with its maximum allowable 01. With regard to the kinematic angular spread of the recoils a large 01 is desirable. The maximum acceptance angle of the spectrometer described in this paper was fixed at about 32 mrad. This corresponds to a solid angle of 3 msr. As illustrated in fig. 10, all recoils of a typical radiative capture reaction are accomodated within such an acceptance. On the other hand, the evaporation residues of a fusion reaction of 32S + l°4Ru near the Coulomb barrier are accepted only at a fraction of about 50%. A large entrance angle is also advantageous with regard to edge scattering. The edge of the aperture must be positioned well outside the cone of multiply scattered projectiles. This consideration becomes particularly important using thick targets. After having passed the entrance aperture, the recoils are transmitted to the detector with a probability (transmission) T = T( O, ~, xT, Yv, q, v, m) which depends on their direction of flight 0, q,, on the location x T, YT at the target where the reaction took place, on their atomic charge q, and on their velocity v and mass m. With a proper average value T the efficiency ~ of the system, defined as the ratio of detected particles to produced ones, can be written as

,=fg.f~. T.a(O,).

C N . nd.

(26)

(relotive)

,

I0

-

(25)

The quantities fg and f¢ are additional correcting factors for the transmission through the various supporting grids and for the channel-plate efficiency. They are assumed to be independent of the distributions of the

with C denoting the counting rate of the recoils of interest, N the projectile beam intensity and nd the target thickness. One obtains fg--0.56 with a transmission of 0.81 of the support grid for the entrance window of the ionization chamber, with a total reduction factor of 0.86 introduced by the grids of the time detector, and with a 0.99 transmission of a grid which defines the sensitive volumes for the A E and EreS measurements in the ionization chamber and, finally, taking into account an rf-shielding grid between the Wien filter and the time detector with a transmission of 0.81. As mentioned above, fc = 0.95 ± 0.05, as determined experimentally by the coincidences between the time detector and the ionization chamber relative to the single rate of the latter. The task of determining T is accomplished by using a Monte Carlo program called T R A M I . In the first part of this program each particle parameter which could possibly influence the transmission is selected according to its statistical probability. The program includes the selection of the recoil direction and energy according to the particular nuclear reaction, the location of the reaction within the beam spot at the target and the selection of the atomic charge. If necessary, the energy losses, the time of production, and the multiple scattering in the target can be included. In a second part of T R A M I , each particle is pursued on its way through the spectrometer to the detector using first order beam optical methods. (A correction for a field admixture of 12-pole structure is taken into account for each quadrupole singlet, although such an admixture is less than 0.5%.) The particles are either removed by one of the apertures or slits, or in fact reach the window of the ionization chamber. In this latter case their energy, charge state or other parameters can be registered to build up an energy spectrum or a charge distribution of the successful particles. This calculated energy spectrum can be compared with the measured one after correction for the energy loss in the entrance window of the ionization chamber and the finite energy resolution. To illustrate the operation of the separator, in fig. 11 some sets of trajectories were plotted employing a special version of the Monte Carlo program. In this program a constant density of particles within the entrance aperture is assumed. The plots indicate the decreasing transmission for charge states different from the equilibrium charge state (15 + ) to which the lens setting was matched.

415

K. Rudolph et al. / The Munich rf-recoilspectrometer

Ld

<~

F~ (D (2"

z

<

N ~~C4

a )VERTICAL

charge state. The lens setting was again assumed to optimize the 15 + state. The fwhm of the transmission curve of nearly six charge states approximately matches the width of the injected charge distribution. The Tq values in fig. 12 refer to a fully o p e n entrance aperture of 8[ = 32 mrad. A smaller 01 would, of course, yield larger Tq values a n d a b r o a d e r charge window. For the calculation of the transmission T the relative (normalized) charge distribution h(q) must be known,

q= 16 ÷

FUSION PRODUCTS b) HORIZONTAL q=lS* c) q=16÷ d) q=14÷ e] PROJECTILES q=lL+ f)

q:7*

Fig. II. Monte Carlo samples of trajectories through recoil spectrometer of fusion products and projectiles with various charge states. Reaction: 32S+ 1°4Ru, E L = ll5 MeV, entrance aperture: OI = 32 mrad. The maximum diameter of the particles within the quadrupole lenses is about 80 mm to be compared to a pole distance of these quadrupoles of 106 mm.

Z

T= ~ h(q) Tq.

The distribution h(q) can be a p p r o x i m a t e d by the semi-empirical formula [17]

h(q) = Nq e x p ( - ½ / 2 / ( 1 + ,qt)}

o.e 0.6

Tq

CtND=Z

( ( v ) 0 /06 1+

~

~M

(29)

according to the formula of Nikolaev and Dimitriev [18] ( v ' = 0.36 c m / n s ) . The width of the distribution is

0.8 0.6

0.4 0.2 1.0

32S+I°4Ru

(28)

with t = ( q - F i ) / O . The p a r a m e t e r Eq describes the a s y m m e t r y of the charge distribution. In practice, the c o n s t a n t s FI, p, a n d cq are determined for each investigated reaction by a m e a s u r e m e n t of the relative transmission of the recoils of interest as a function of the focusing power of the lens, which is then fitted to the above formula. Fig. 13 shows a typical result of such a fit. It refers to fusion products of the reaction 36S o n I°4Ru at E L = 100 MeV. A reasonable fit (curve a in fig. 13) was o b t a i n e d using q -- qNo -- l with

In fig. 12 the charge d e p e n d e n c e of T is shown more quantitatively• Here the transmission Tq of particles of a given charge state is displayed as a function of the

I.C

(27)

q--I

rel t r a n s m i s s i o n 4 ~ ~

o •t 8 12 16 20 2/, 28 32 charge sto~e

0,~ O.E O.l. 0.2 Field gradient of I. si.nglet

o.~

112 0.2

,;. )~" )i÷ ,;+ ,'8- 2'o~

q

atomic charge

Fig. 12. Calculated transmission Tq for a given atomic charge state q averaged over all other Monte Carlo parameters. Assumed reaction: 32S+ l°4Ru at 115 MeV. The lens triplet was set for optimum focusing of the 15 + state.

lit

~'.o o19 0'.8 o17 o'.6 o'.5 &

kGausslcrn

Fig. 13. Measurement (points with error bars) of the relative transmission of evaporation residues from the reaction a6S + ]°4Ru at E L = 100 MeV as a function of the focusing strength of the triplet lens. Curve a: Monte Carlo calculation of relative transmission with fitted parameter ~/, p and~q of the charge distribution (see text). Curve b: Same as curve a, with symmetric charge distribution ( % = 0 ) . Insert: Charge distributions obtained from the fitting procedure.

K. Rudolph et al. / The Munich rf-recoil spectrometer

416

Te

To" sin e /~\

/

\

0.8 0.6 o.4

ii

\\\\

xlO.3 io 8 6

\ _\\

0.2

\

,

,

,T

10

20

30

40

2

50 8 (mrad)

Fig. 14. Monte Carlo calculated relative transmission as a function of recoil direction. The decrease of the transmission with increasing 0 is mainly due to the limited focusing of the various charge states. Assumed reaction and charge distribution: see text.

determined by the p a r a m e t e r p = 3.6 corresponding to a fwhm = 1.09 ¢ ~ . The asymmetry p a r a m e t e r turns out to be Cq = 0.5. The m a x i m u m of the charge distribution lies very close to g/ND. Experience indicates a slight d e p e n d e n c e of the charge distribution on the target material. The charge dependence of the particle transport leads to a decrease in the transmission with an increasing angle 8 at injection. A recoil nucleus entering the spectrometer at a large 0 has a small chance of reaching the

32 S + Counts 6000

r_

/

I°1*Ru

115 M e V

I-----'7 Recoils Injected at I Iris Aperture I (calculated) ~ l l

detector if its atomic charge deviates m u c h from the one to which the lens is tuned. In fig. 14 the function ~ is plotted, where ~ is the transmission simulated by the M o n t e Carlo calculation for a recoil with an entrance angle O. The calculation is based on the fusion reaction 32S + l°4Ru at 1 15 MeV. A G a u s s i a n charge distribution with o = 0.32V~ has been used. Fig. 14 shows that the area-weighted transmission T ( 0 ) s i n 0 is still large near the aperture cut-off at 0~ = 32 mrad. The velocity window (relative transmission as a function of particle velocity) is not only a property of the i n s t r u m e n t alone, b u t also depends on the angular and charge distribution of the particles considered, and hence on the nuclear reaction u n d e r investigation. Fig. 15 shows the transmission of fusion recoils T ( v ) from the 32S on 1°4Ru reaction considered before. The function T ( v ) is the result of a M o n t e Carlo calculation which simulates the successive recoils of neutrons, protons and a-particles evaporated by the fused nucleus according to a standard statistical c o m p o u n d nucleus de-excitation theory. T ( v ) is a p r o p e r average over other M o n t e Carlo parameters such as direction, target position, and atomic charge of the particle. In addition the figure displays the result of the M o n t e Carlo calculation of the velocity distribution Ho(v ) of the evaporation residues entering the entrance aperture. Free parameters in such a calculation are the relative intensities of residues having evaporated neutrons only, o r one a-particle and some neutrons, or one p r o t o n plus neutrons, respectively. These relative intensities could be determined by a

I ' I---1

Transmission

"T(v)

I I

, I 0.5 Transmission r I----~ I cx-Evaporation I ~/~--~ ! "_ ! ~ Residues 1.000 I // r -J Transmiffed-] -~, F-"/'/-q ( x 50 } 0.L o(-Evaporation ~/' I P~r-nil¢ I /N I / ! /I ~. . . . . . . ; i \ I / I Res dues / I i, ~ L- ' ~ \ ' I JL 0.3 I (xSO) i ./~-J I~ , J k II I L-3\/ -] 200( F-[~L//I L_ I I II 0.2 ~, , ! I r l~.i~ N p.,ifrnn q --"I , I ~-J I I I I , .Y --J , I anN%'~F~;~ I , I J \ , l//\ ~ F--~-IFvA'nnr'n'f~'n'n '' L~L-n, ~ rE. \L-n 0.1 ~-~/ I i~ i I -~EL~;12I L_~ - I \! . ' ~ . 4 _ < _ ~ ? J , .~_.~4-7 , ~°'~, , ~L4__, ,~-L~_.'.-n, 0.50 0.51. 0.58 0.62 0.66 0.70 0.71. Velocity cm/ns Fig. 15. Comparison of the calculated transmission, T(v) as a function of recoil velocity, the calculated velocity spectrum Ho(v ) entering the recoil spectrometer and the corresponding measured velocity spectrum Hob~(V) of transmitted recoils. The relative intensities of a-, p- and n-evaporation residues (in all cases plus additional neutrons) were fitted to Hob~(V) to calculate the spectrum of the injected particles H0(v). Except for statistical deviations, it is Hob~(v) = T(v). H0(v). The experimental velocity resolution is distinctly less than the channel width of the histogram.

K. Rudolph et al. / The Munich rf-recoil spectrometer statistical theory. However, due to the uncertainties of the parameters needed in such a calculation they were obtained in the present case by fitting the expected velocity spectrum Tv" Ho(v) to the observed one (Hobs(V)). The observed velocity spectrum Hobs(V) is also shown in fig. 15. For a satisfactory measurement of the relative intensity of the a-evaporation residues the velocity window must be shifted to higher (or lower) velocities by a proper setting of the rf-phase, and the fitting procedure must be repeated. The example of a velocity spectrum and the corresponding transmission discussed above demonstrates that the recoil spectrometer is suited to measure fusion cross sections, in spite of the limited acceptance of the instrument.

6. Operation and calibration The operation of the relative complex recoil spectrometer is simplified by a computer control of the field settings of quadrupoles, dipoles, and electric field as well as of the rf-phase. This is accomplished with the help of an on-line program running on the PDP-15, which serves as a standard data station within the Munich PDP-10 system. The rf-phase is calibrated to within -+0.5 ns by a simple determination of that particular phase (between beam pulsing system and spectrometer-rf) which allows the direct particle beam to pass through the filter to a quartz centered in front of the ionization chamber. The quadrupole strength is adjusted close to the maximum of a distribution measured according to fig. 13. At this setting the transmission is largely independent not only of the exact quadrupole field, but also of the exact field ratio of the ~,elocity filter. The electric field amplitude is kept constant to within 0.5%, and the phase to within 0.5 ° relative to the high energy chopper of the tandem beam pulsing system. The time zero for the recoil time of flight measurement is calibrated by observing the arrival time of the projectiles at the time detector. To reduce the beam intensity from 1011-1012 particles/s to a manageable rate of 103/s without changing the time and energy profiles of the beam, the switcher magnet current is readjusted to allow one of the charge exchange components of proper intensity to pass. The same projectile particles can also be used for an energy calibration of the ionization chamber. Data taking is carried out under pile-up and dead time control. Coincidences (also partial coincidences) of the AE-, Eras- , channel plate- and position-signals are recorded. Two semiconductor counters mounted at a distance of about 150mm from the target above and below the optical axis serve as beam monitors and allow the measured recoil counting rates to be based directly

417

on the Rutherford scattering cross section. The vacuum, particularly in the vicinity of the rf deflector, is kept below 10 -7 mbar. At higher pressures X-rays from accelerated electrons between the deflector plates can produce an intolerable "noise" background of the channel plates by photoelectron production at the carbon foils of the time detector. Ionization chamber gas leaking through the entrance window is pumped by a 3800 f/s cryo pump. The simple geometry and field structure of the whole system, as well as the precise stabilization and calibration of the lens and the filter elements, result in a very satisfactory reproducibility of the counting rates and spectra as experienced during several different experiments. The precision of absolute cross sections depends on a number of uncertainties such as beam current density distribution at the target, atomic charge and angular distribution of the recoils, and alignment of components. Their influence must be analyzed for each particular investigation. Two examples of an experimental test of the Monte Carlo calculations for the transmission are indicated in the figs. 16 and 17 (ref. 7). In the first case, reactions of 160+ 1 2 C ~ 2Z,Mg(9.53MeV) + cx

%

E L = 5 3 . 5 MeV

80 70

7mrod

60 50 40 ' ~ =

14mrad

30 20 10 Field grodient of I. singlet t!

,

~

,

!

I

I

1.2 1.0 0.8 0.7 0.6

kGouss/cm

x

Ring detector

Entrance aperture of RS

Fig. 16. Comparison of measured and calculated absolute transmission T of the recoil spectrometer as a function of the ' field gradient of the first singlet. Experimental points: Detected 24Mg nuclei in coincidence with backward emitted a-particles for two different solid angles. Curves: Monte Carlo calculated transmission assuming a Gaussian charge distribution centered at q = 9 + with a fwhm of Aq = 2.63, no fits.

418

K. Rudolph et al. / The Munich rf-recoil spectrometer

60

160+ 12C ~ 27Al(18.541'4eV)+ p L26AI(7+)+ n 56

We are indebted to Dr. R. Pengo for performing the detailed calculations with the M o n t e Carlo program and for further developments of this program. We would like to give credit to the staff of the Institute's workshop represented by Mr. W. G r o t z and of the T a n d e m L a b o r a t o r i u m represented by Drs. H. Mtinzer and L. Rohrer for their p e r m a n e n t excellent support. This project is supported by the Bundesministerium fiir Forschung und Technologie.

/'~ l~ 1

4C { ~ ac

2c ioj 1.52

1.56

1.60 26A[ recoil velocity

1.64

1.68

1.72

References

cm/ns

Fig. 17. Velocity spectrum of 26A1 recoils. Comparison of the distribution of coincident events with backward emitted protons with calculated velocity distribution. The primary velocity of the 27A1 recoils is v = 1.61 cm/ns. The time window was centered at 1.63 cm/ns.

12C + 1 6 0 populating the 9.53 MeV state in 24Mg are selected by detecting the accompanying a-particle in a ring detector near 180 °. F o r each observed a-particle a corresponding 24Mg recoil of k n o w n velocity travels within a well-defined cone into the recoil spectrometer. The transmission of these recoils is given by the ratio of the coincidence rate (ring detector and ionization chamber) to the singles rate of the a-particles. Fig. 16 shows the measured transmission for two different solid angles 0max (defined by the distance t a r g e t - r i n g detector) as a function of the lens setting. The calculated transmission is also shown for comparison a n d demonstrates the excellent agreement with the m e a s u r e m e n t to within a b o u t 10%. In that particular experiment the distance L from the target to the deflector plates (2.6 m) a n d the total distance to the ionization c h a m b e r were unusually large, with the resulting rapid decrease in transmission already at an acceptance angle of 7 - 1 4 mrad. In fig. 17 a somewhat different case is shown. The system ]2C + 160 decays to the 18.54 MeV state in eTA1 by p r o t o n emission. The p r o t o n is again observed by a ring detector at 180 °. The recoiling 27A1 emits a n e u t r o n which populates the 7 + at 3.92 MeV excitation in 26A1. The neutron carries a relative energy of 1.56 MeV. A n e u t r o n emitted perpendicular to the b e a m pushes the 26A1 recoil in a direction n o longer accepted by the entrance aperture of the recoil spectrometer. Emitted in forward or b a c k w a r d direction, it modulates the velocity of the recoil as shown in the figure. The difference in intensity of the two peaks can be understood by solid angle t r a n s f o r m a t i o n arguments and by a slightly asymmetric position of the velocity window. In fig. 17 the measured a n d calculated n u m b e r s of 26Al-recoils are compared. With relatively poor statistics the agreement between calculation and m e a s u r e m e n t is again very good. In particular, the calculations reproduce the shape of the velocity spectrum.

[1] H.A. Enge, H.D. Betz, W.W. Buechner, L. Grodzins, W.H. More and E.P. Kanter, Nucl. Instr. and Meth. 97 (1971) 449. [2] H. Ewald, K. Gtittner, G. Mtinzenberg, P. Armbruster, W. Faust, S. Hofman, K.-H. Schmidt, W. Schneider and K. Valli, Nucl. Instr. and Meth. 139 (1976) 223; G. Mtinzenberg, W. Faust, F.P. Hessberger, S. Hofmann, W. Reisdorf, K.H. Schmidt, W.F.W. Schneider, H. SchOtt, P. Armbruster, K. Giittner, B. Thuma, H. Ewald and D. Vermeulen, Nucl. Instr. and Meth. 186 (1981) 423. [3[ M. Beckermann, J. Bell, H.A. Enge, M. Salomaa, A. Sperduto, S. Gazes, A. DiRienzo and J.D. Molitoris, Phys. Rev. C23 (1981) 1581. [4] H.A. Enge, Nucl. Instr. and Meth. 186 (1981) 413. [5] S.J. Skorka, K. Rudolph and J. Hertel, GSI-Bericht 73-3 (1973) 1. [6] P. Konrad, D. Evers, K.E.G. L6bner, U. Quade, K. Rudolph, S.J. Skorka and I. Weidl, Zeitschr. f. Phys., to be published; P. Konrad, Thesis (1980) University of Munich. [7] I. Weidl, D. Evers, P. Konrad, K.E.G. L6bner, U. Quade, K. Rudolph and S.J. Skorka, Phys. Lett., to be published; I. Weidl, Thesis (1982), University of Munich. [8] D. Evers, K. Rudolph, I. Weidl, P. Konrad, U. Quade, K.E.G. LObner and S.J. Skorka, XIX. Int. Winter Meeting on Nuclear physics, Bormio, 1981; R. Pengo, D. Evers, K.E.G. L6bner, U. Quade, K. Rudolph, S.J. Skorka and I. Weidl, to be published. [9] S.J. Skorka, Proc. 3rd Int. Conf. on Electrostatic accelerator technology, Oak Ridge, 1981, p. 130. [10] S. Morinobu, 1. Katayma and H. Nakabushi, Proc. 4th Int. Conf. on Nuclei far from stability, HelsingeCr, 1981, Report CERN 81-09, p. 717. [11] T.M. Cormier and P.M. Stwertka, Nucl. Instr. and Meth. 184 (1981) 423. [12] B. Kohlmeyer, W. Pfeffer and F. Piihlhofer, Nucl. Phys. A292 (1977) 288. [13] K. Rudolph and D. Sch6dlbauer, Nucl. Instr. and Meth., to be published. [14] U. Quade and K. Rudolph, Nucl. Instr. and Meth., to be published. [15] H. Sann, H. Damjantschitsch, D. Hebbard, J. Junge, D. Pelte, B. Povh, D. Schwalm and D.B. TranThoai, Nucl. Instr. and Meth. 124 (1975) 509. [16] U. Quade, K. Rudolph and G. Siegert, Nucl. Instr. and Meth. 164 (1979) 435. [17] R.O. Sayer, Revue de physique appliqube 12 (1972) 1543. [18] V.S. Nikolaev and I.S. Dimitriev, Phys. Lett. 28A (1968) 277.