* W P * ^ * ^ ANU-P/1054 ,

LENS MODE OPERATION OFA SUPERCONDUCTING ELECTRON SPECTROMETER IN (HLxn) REACTIONS

T. KTO^DI, G.D. DRACOULIS AND A.P. BYRNE

Department of Nuclear Physics, Research School of Physical Sciences Australian National University, GPO Box 4, Canberra ACT 2601,

Australia

Accepted for publication .n Nuclear Instruments and Methods in Physics Research

LENS MODE OPERATION OF A SUPERCONDUCTING

ELECTRON SPECTROMETER

IN (HI,xn) REACTIONS

T. KIBEDI1, G.D. DRACOULIS AND A.P. BYRNE

Department of Nuclear Physics, Research School of Physical Sciences,

The Australian National University, GPO Box 4, ACT 2601 Canberra,. Australia

Abstract: An electron spectrometer, consisting of a superconducting solenoidal

magnet transporter and Si(Li) detector, is described. The spectrometer has been used

in lens mode, with an envelope baffle system and with the field swept under computer

control. The efficiency obtained for the optimum energy at a given field is ~ 5.9(5) %.

Model calculations have been carried out to describe the transmission and efficiency of

the swept lens, as well as the effect of the electron angular distribution on conversion

coefficient determinations. The performance of the spectrometer has been tested with

radioactive sources and several in-beam experiments using (HI,xn) reactions.

1) National Research Fellow; permanent address: Institute of Nuclear Research of

the Hungarian Academy of Sciences, H-4001 Debrecen Pf 51, Hungary

1

1. Introduction

Conversion electron spectroscopy is an important method of determining multi-

polarities of nuclear transitions. With (HI,xn) reaction?, the main difficulty encoun­

tered is the high flux of prompt low energy atomic electrons knocked out following

charged particle interactions in the target. Measures to reduce this problem (such as

the use of absorber foils) can lead to degraded resolution. The resolution, in general,

is limited by energy straggling in the relatively thick targets, necessary to stop the

recoiling nude- The spectrum quality and consequent sensitivity are also affected by

the electron detector response (peak-to-total), 7-ray interactions in the detector and

scattering of 7-rays and electrons from surrounding material, as well as the contin­

uum from /?-decay of the reaction products. All make a significant contribution to

the background.

Different types of /?- spectrometers have been used for in-beam studies but in the

past decade a number of solenoid-type instruments [1-8] have been developed. An

important advance [1] in the use of the combination of solenoid transporters and

Si(Li) detectors was provided by the inclusion of specially designed baffle systems, in

association with different field profiles, enabling three different modes of operation,

depending on the physical problem to be investigated. The first is the broad range

mode in which a low energy transmission cut-off is performed by a small disk placed

between target and detector, or by locating the detector off-axis. The second is

the lens spectrometer mode in which an envelope baffle system selects a restricted

momentum band; to cover a large energy range the magnet current is swept. In the

third mode - the recoil shadow method - a longitudinal, semi-cylindrical solid baffle,

2

inserted between target and detector, selects delayed electrons emitted in flight from

recoiling nuclei. (The solenoid spectrometer can also be adapt<*i for in-beam studies

of internal-pair transitions [9].)

Here we review the development of the lens mode operation of the superconduct­

ing, solenoidal, electron spectrometer at the Australian National University. The

spectrometer is in regular use for spectroscopic studies, to date ma;nly with reactions

induced by beams of boron, carbon and oxygen.

2. Description of the spectrometer

2.1. Superconducting solenoid

The superconducting solenoid l consists of inner (target) and outer (short and

long end) coil pairs as shown in fig. 1. The coils are surrounded by a liquid helium

reservoir and a thermal shield cooled by liquid nitrogen. (Electron detectors can be

connected to flanges located 309 mm (short end) and 459 mm (long end) distant from

the target, at the ends of the transport tube.) The bore of the transporter is at room

temperature and has a diameter of 85 mm, large enough for the convenient insertion

of baffles, shadow shields, particle and standard germanium detectors. There are

three, 30 mm wide, gaps in the vertical plane for the beam entrance and exit, an,! for

introduction of the target.

The target holding system is connected to the base of the spectrometer and allows

adjustment of target height and angle (with respect to the beam). Targets can be

interchanged through a vacuum luck.

'Cryogenic Consultants Ltd. London, England

3

The coils are pre- ooled by liquid nitrogen and usually left overnight to stabilise

at 77 K. Following expulsion of the remaining nitrogen, the system is filled with

liquid helium. The liquid helium Dewar (10/ capacity) is located on the top of the

spectrometer (close to the long end). Cooling to A.'IK takes about 2 hours and the

helium holding time is typically 20 hours with a field lower than 0.5 T. Subsequently

the reservoir can be re-filled in about 10 minutes.

2.2 Fie!! profiles

The target, short and long end coil pairs can be powered separately, to provide

a variety of field profiles (see fig. 1). (In the lens mode, all coils were connected in

series to a single power supply.) The maximum current of 50 A corresponds to a 2.03 T

magnetic field at the position of the target. The axial (z) distribution of the field (see

fig. 1 curve a), measured with a 3-axis gaussmeter showed a small inhomogeneity of

-3.7% < AB/B < +16% in the -175mm < z < +350mm interval. The measured

values agreed with the field calculations performed with the MCAMOS code [10] and

were used for the electron trajectory calculations.

A different field profile (fig. 1 curve b) was also tested. In this configuration, the

coils at the short end of the solenoid (on the opposite side of the target from which

electrons are viewed by the lens) are turned off so that the field drops rapidly in this

region. The field at a Ge detector inserted into the bore (~ 10cm from the target)

would be < 0.057.

4

2.3. Computer control

The high stability power supply is operated by remote programming using a

PDPl 1 computer and a 12 bit digital-to-analog converter (DAC). To measure conver­

sion electrons with the lens in a wide energy range, the field is swept between lower

and upper limits. The computer code steps the output voltage of the DAC after a

certain beam charge (measured with a current integrator), or time interval in the

case of a radioactive source, or any other parameter of choice fed into a computer

readable scaler. The computer control program approximates the required form of

the dependence of the magnetic field on the total beam charge (or time) by small

steps, typically ~ ZmA and ~ 0.0001 T in curren» and field respectively. The maxi­

mum sweeping speed is limited to ~ 0.07 T/min because of the possible lag between

the magnetic field and the control voltage caused by the impedance of the solenoid

system. At this speed the measured lag, available from analysis of the event-by-event

data described in section 2.7, is equivalent to less than 1 % in field, expressed as a

proportion of the momentum window. Computer control simplifies the selection of

lower and upper field limits (as shown later, to optimise efficiency in selected regions),

the unit of beam charge collected or time spent between steps, as well as the field-

stepping function - in the simplest case, of triangular form. A Hall-probe is inserted

into the solenoid tube to measure the magnetic field.

2.4. Baffle system

The baffle system of the lens spectrometer consists of two axially mounted ab-

5

sorbers, a diaphragm and a spirally-cut paddle wheel baffle (see fig. 1). Electrons

are detected after raversing two orbits - a "two-loop" V Se system. As positrons

differ in their spiral direction from electrons, they are suppressed by the paddle wheel

baffle. To design the baffle system, detailed calculations were carried out with an

advanced version of the LENS code [3]. The program calculates electron trajectories

for 4 given energy (£) and magnetic induction (B) with emission coordinates {r,z

and d for location; 6 and • for the angle of the velocity) generated randomly. After

a small displacement along the z-axis {Sz < 0.5 mm) the trajectory is ehecked for

i;..erception by the baffle system. To obtain sufficiently accurate estimates of the

transmission, more than 10000 trajectories were calculated for every field and energy

combination.

Two different physical models were used. In the (nearly) homogeneous field ap­

proximation the electrons move on helical paths. The radius (p) and the velocity

angle (0) are obtained from the formula:

1.704433 x l0-3TmVE* + 2mo<?E {Bp)E = — , (1)

where Bp is the magnetic rigidity for electrons and ntoc3 is the electron rtrt mass en­

ergy. The relationship between the average orbit parameters at two different positions

(t and i + 1) along the symmetry axis is

Bi 3\n$i Pi Ti - - - —^ • (2)

Bi+i Siti#i+i Pi+l r i + l

A more realistic model is based on direct numerical integration of the equations

of motion [3,11]:

f » - i / v B , + r<f2 (3) m

z = -5-rjB, (4) m 6

iV + 2ryj = —(iBT - rB x ). (5)

m

Solutions of these differential equations were obtained using the Runge-Kutta method.

The Br(r,z) and fl.(r. r) field components were obtained by two-dimensional La­

grange interpolation between 16 neighbouring calculated values, tabulated in grids

(with spacing Ar = 5 mm; Ar = 5mm).

The baffle system was designed to provide maximum transmission and background

suppression. Some characteristics of the lens system are listed in table 1. The axial

baffles were fabricated from lead and supported with thin rods. The diaphragm and

paddle-wheel baffle are constructed from stainless steel (non-magnetic type 316).

2.5. Electron and gamma-ray detection

A 200 mm3 area and 2.9 mm thick Si(Li) detector is used as the energy disper­

sive element. The detector, which is connected to the long end of the transporter,

is kept d'- liquid nitrogen temperature. To measure the 7-spectrum simultaneously

with the conversion electrons, a high-purity germanium detector is installed in the

vertical plane, at 135s to the beam direction about 25 cm from the target. The de­

tector is surrounded by a Nal(Tl) shield to suppress Compton-scattered events, in

an arrangement similar to that described by Byrne and Dracoulis [12].

2.6. Beam optics and target selection

The spectrometer is connected to the beam line 3 m beyond a magnetic quadrupole

pair, focussing lens. The only collimator (made from lead) has a 3 mm hole and is

7

located 50 cm before the target. It can be moved in the vertical direction in the

event of beam defection in the field of the solenoid, although in the lens mode (B <

0.2 T) no significant beam deflection was observed. The tead beam stop, located

approximately 50 cm from the target, is electrically isolated to measure the beam

current.

Following (Hl.xn) reactions, the de-excitation lines from the residual nucleus are

affected by Doppler-shifts and broadening if they are emitted before the nucleus stops

in the target, or if it exits from the target. Since the electron resolution is controlled

by the target thickness and target angle, a Monte-Carlo code was used to calculate the

stopping of the residual nuclei, as well as the energy loss and broadening of conversion

electrons. In our experiments usually 1 — 2.5 mg/cm2 thick targets were used and the

target angle was ~ 30". Because most of the recoiling nuclei are stopped no significant

line broadening was observed.

2.7. Data collection and analysis

A block diagram of the signal electronics is shown in fig. 2. Most experiments are

carried out using a pulsed beam, hence electron and 7-ray times with respect to the

beam puise are measured in a common time-to-amplitude converter. For each valid

electron signal two measures of the field are obtained by converting the analog DC

level from both the voltage controlling the solenoid power supply (produced by the

DAC), and the output of the Hall probe sensing the field, into pulses, related in time to

the detected electron. Up to five signals are then processed - either a 7-ray energy and

its associated time, or an electron energy, its time and the two associated measures

8

of the field. All data are collected in event-by-event format and written to magnetic

tape for subsequent off-line analysis. The off-line analysis consists of the selection of

momentum-matched electron events and the construction of corresponding electron-

time and 7-ray-time matrices. Projections from these matrices lead to (momentum-

selected) electron and 7-ray spectra in corresponding time regions. Ek-ctron and 7-ray

intensities are then extracted by the fitting of line-shapes to the spectra.

3. Calibrations

The energy, momentum window, transmission and swept-efficiency calibration

were determined initially using I 5 3 £ u and inTa sources. The diameter of the ac­

tivity was 3mm, similar to that of the beam-spot. Two different field profiles were

tested (fig. 1 curve a and b), both of which result in nearly the same performance.

All calibration data given in this paper refer to the inhomogenous field profile (curve

b in fig. 1).

3.1. Momentum selection

An important advantage of the lens spectrometer is that, at a given magnetic field,

only a part of the full electron spectrum, with a well-defined relation between electron

energy (E) and solenoid field (B) is transported to the Si(Li) detector. To determine

this relationship over the full energy range, an E — B matrix was constructed by

sorting of the electron events obtained with the m £ u source. Projections on the field

axis were made by gating on conversion lines in the energy spectrum. A typical field

9

spectrum, gated by the electron peak at 294 ktV (344 A' line of i s 2 £ u ) is shown in fig.

3. The nearly Gaussian distribution reflects the momentum window of the lens. (For

direct comparison with the calculated form of the momentum window the spectra

have been normalized to the same total area.) Three field values are marked in fig.

3. £?i„„. BmprfT and the field at maximum yield, Bmmz.

Some events fall outside the expected momentum window, evident above Bnrrrr in

fig. 3. mainly because of backscattering of electrons from the detector and scattering

of electrons on the baffle system. The tail occurs OR the high field side since a

given partial energy deposited in the detector results from electrons of higher initial

energy, transported therefore at higher field. A few other electrons occur outside

the window because of electrons produced by interactions of 7 rays and secondary

electrons produced by scattered particles. Momentum selection is used to remove

such incomplete events from the electron data set and therefore from the electron

energy spectrum.

The experimental values of Bi,m^,Bmmx and Btpf€r values obtained for 1 5 3 £ u

conversion lines are displayed in fig. 4. From eq. (1) one can deduce the three B,(E)

dependences

B.(E)=Cix(Bp)E. (6)

By fitting this function (curves in fig. 4) to the experimental values, the C, coefficients

listed in table 1 were obtained.

In the analysis all [E, B\ events which fulfil the criterion

Bi0Vtr(E) <B< Bupptr(E) (7)

are selected.

10

The proportion of non-matching events with the , M £ « source n ~ 20% of the total,

a value close to the average backscattering probability. The high energy region of the

electron spectrum from the T a source, after momentum selection, is shown in tig.

5. Except for the low-intensity, high-energy & branches mainly conversion electrons

are expected. For the 1121.3 keV K line the peak-to-background ratio obtained is

53:1.

• •

3.2. Efficiency calibration

The efficiency of the spectrometer for a given energy (E) and magnetic field (B)

is

7(£,s,n,e.#; = T(E7B,n,o,*) X [I -piE,QD)-t(E.eD)\, ($)

where T{E,B,tl,Q,+) is the transmission probability for an electron emitted in the

direction of 6 and *, p(£,6&) is the probability of backscattering of the electron

from the detector, i(£, 8©) is the transmission probability through the detector and

6 0 i* the angle of incidence of the electron on the detector face. (For simplicity, the

variables of the emission point (r, z and 4) are denoted with ft.) In the LENS code

the functions p\E,%o) and ( (£ ,60) are approximated with s*mi-empirical formulae

fitted to the available data [13,14]. The finite size of the source was taken into

account in the model calculations, but target effects (self-absorption and scattering)

were neglected.

In the lens mode the f»cid is swept between values B\ and B% to transport electrons

from a (chosen) wide energy region. The swept efficiency (7 m (£ ) ) can be obtained

11

by integration of eq. (8):

V™(E)=f f T}(E,B,<ly6,*)dndB. (9)

After numerical integration it can be approximated by

ifc»(£) = Ne x Ttul(E) x [1 - p(E, SF) - r(£, ©^)], (10)

where TSW(E) is the swept transmission:

T„(E)~(Bp)B, \ (ID

0D is the average detect. . —igle and Ne is a normalization factor.

The experimental efficiency values (rtf^E) = Ac/Ie) determined with ls2Eu con­

version lines are shown in fig. 6, where Ae and Ie are the peak area and the known

peak intensity [15], respectively. The experimental efficiency versus energy function

(solid line in fig. 6) was obtained by a fit of the rjtvl(E) function (eq. (10)), scaled

by the single normalization factor, Ne. This factor is then determined for the present

spectrometer configuration, sweep range, source strength and measuring time.

The efficiency curve was confirmed using the continuous spectrum of ^"-transitions

from 152Eu. The measured f}~ -spectrum was corrected for the efficiency and detector

response. Experimental values of the Fermi-Kurie plot were fitted [16] by straight lines

using the most intense, known ^"-transitions (Q0 = 386, 696, 1064 and 1475 keV).

The fitted and measured /?~-spectra are shown in fig. 7.

The efficiency of the spectrometer is well determined in the 70 - 1400 keV energy

range. The loci in fig. 4 are then used to determine the lower and upper field limits

3\ and Bj, necessary for the efficiency defined by eq. (10) to be valid for the selected

energy region between E\ and E?.

12

In some on-line experiments only a part of the full energy spectrum is important,

so that the magnetic field can be swept between the restricted range fl£n~'me and

£on-/tne> t j j U S e n n a n c i n g t n e efficiency. A simple re-normalization formula is applica­

ble to obtain the efficiency with respect to the original calibration:

Dcalib Dcalib

V2~hnt(E) = flon-Jme _ gan-tine X llt^) * (12)

where A"'*6 - B| 0'' 6 was the field range used in the calibration.

The efficiency of the 7-spectrometer was determined by a 5-parameter polynomial

fit to the experimental values obtained from the measured 7-ray intensities.

Since the 7- and conversion electron spectra are recorded simultaneously and ab­

solute electron and 7-intensities were used to calibrate the spectrometers, the exper­

imental conversion coefficient is a< = /,//>, where i denotes a specific electron shell

(K, L or A/). The calibration of the spectrometers (that is, both 7-ray and electron

efficiencies) and a< determination are confirme . by fig. 8, where the ratio of known

conversion coefficients (aknown) to measured values (a e*p) is shown. The measured

values were obtained from different experiments (both on-line and off-line) and with

different target thicknesses, involving substantially different electron lineshapes. In­

dependent of these evaluations, efficiency calibrations are routinely carried out for

each experiment.

A feature of the computer control of the lens spectrometer (compared to the

use of an electro-mechanical device) is that the form of the rj,w{E) function can

be easily modified. Although the efficiency is an increasing function of the energy

(partly compensating the decrease of the converr'on coefficient), in a typical electron

spectrum most of the intensity is concentrated at lower energies. To obtain sufficient

13

statistics for high energy lines, very long measuring times might be required. This

disadvantage could be avoided by stepping the magnetic field after, for example,

quadratic increases in beam charge. In this way the lens would transport relatively

more high energy electrons (and fewer low energy ones). The corresponding form of

the efficiency function can be obtained by a transformation of eq. (10).

Angular distributions *

It is well known that, just as in-beam 7-rays exhibit an angular distribution be­

cause of nuclear alignment caused by the reaction process, in-beam conversion elec­

trons also exhibit angular distributions. Since these distributions can affect the mea­

surement of conversion coefficients (by distorting intensities compared to those de­

termined from source calibrations) they must be taken into account. The formalism

describing the electron angular distribution has been recently reviewed by Faust [17],

therefore only the main equations (assuming, for simplicity, pure multipolarities) will

be quoted here.

If the angular distribution for 7-rays is written as

W,(0) = 1 + A2(-,)P2(co*Q) + A4(-,)P4(cosQ), (13)

the corresponding form for conversion electrons is

W.,(0) = 1 + A3('()b2(tl)PJ(cose) + A4(f)b,(ei)P4(cose), (14)

where the Ak{f) are the angular distribution coefficients for 7-rays, P*(cos 0) are the

Legendre polynomials and 0 is the emission angle with respect to the beam direction.

The bk{et) = bk{nLn'L',ti) coefficients are the normalized directional particle param-

14

eters, which depend on the transition energy, on the multipolarity (vLir'L') and on

the specific electron subshell (ej [18].

The 7-ray and electron angular distributions are in general attenuated so that

••*r(7) = Ofc^*(7)4W(7) and A^fa) = akQk(ei)At£"'(ei), where ^ w ( 7 ) and

/ U k e p r ( e i ) a i c values for maximum alignment and Qk(l) and Qkfe) are the geomet­

rical attenuation coefficients. The ak coefficients describe the reduction of alignment

caused by (a) the population of substates from higher levels, (6) neutron evaporation

and (c) perturbation by magnetic dipole and electric quadrupole fields. The geomet­

ric attenuation factors depend on the solid angles involved so that Qk(l) and Q*(e)

differ. (The electron angular distribution is also affected by electron scattering in

the target which we neglect.) The form of eq. (14) describing the electron angular

distribution measured with a spectrometer whose symmetry axis is located at 0 with

respect to the beam, is

We,(Q) = 1 + a2Qi{e)Af"r(i)b2(ei)P2{coie) + a4Q4(e)At

4

u"(i)b4(ei)P4(a»e).

(15)

The solid angle attenuation coefficient of the electron spectrometer can be obtained

[19] from

o n = I%Jg'l(E,B,fl,en*)Ph(coie,)dndB W k [ e ) f%fati{E,B,tl,e„9)dSldB ' l '

where 0 , is the emission angle with respect to the solenoid axis. After numerical

integration values of Qj(e) = 0.820 and Q4{e) = 0.483 were obtained. These are spe­

cific to the present baffle geometry and field configuration as discussed further below.

According to the model calculations the energy dependence of Qk(e) is negligible.

Since the 7-rays are detected at ~ 135° to the beam direction, the angular distri­

bution effect for the determination of Iy is small. The corrected electron intensity is

15

given by

/. =/.(e)/we.(e) (17)

Typical values of WK(Q) are shown in table 2 for the current arrangement with

the solenoid axis at 90° to the beam. According to table 2 the relative deviation from

an isotropic distribution is < 20%. Also shown in the table are the values obtained

with an alternative arrangement of the spectrometer with parallel beam entry (0° or

180°). It is seen that in these geometries the distortion due to distribution effect are

larger.

The value of the Qk(e) solid angle attenuation coefficient can be calculated, in first

approximation, from the extreme acceptance angles 0 , , m j n = 11° and 0 t , m O x = 32°

(with respect to the solenoid axis). The sensitivity of the spectrometer to the electron

angular distribution could be reduced further by increasing these angles, principally

by reducing the target-detector distance. For example, for a similar solenoid, but with

a 25 cm target-detector distance, and 0,,mi„ = 11°, 0,,m<»x = 48° a value of Qi(e) =

0.64 was obtained [20].. However, the present spectrometer is used for spectroscopy

following (HI,xn) reactions where recoil velocities are significant and relatively thick

targets are used. The extreme angles and the target-to-detector distance were chosen

to optimize the performance of the spectrometer given these conditions.

5. Experimental results

The spectrometer is in regular use and a considerable number of experiments have

been performed, including the measurement of the conversion electron spectra of

nuclear transitions in 1800s, 2l0'211-2URn, 2U21iRa and 2u™Fr nuclei. In each case,

16

conversion coefficients for relatively weak transitions have been obtained. In most

experiments a pulsed beam was used to separate prompt and the delayed transitions,

thus reducing the complexity of the spectra.

The effect of momentum selection is illustrated in fig. 9 for conversion electron

measurements of transitions in lt00s. populated using the , 6 8 Er( , 6 0 ,4n) reaction at

87\ltV [21]. The target was a rolled 1.3 mg/cm2 foil, enriched to 96% in I 6*£r,

with ~ 1.5 mg/cm2 lead evaporated on the rear surface. The target angle was ap­

proximately 30° to the beam direction. According to the calculations > "80 % of the

reaction products were stopped in the target. The counts in the background spectrum

removed by momentum selection (i.e. not fulfilling the criterion described by eq. (7))

are ~ 27% of the total .

An enhancement in efficiency, an increase of 3.8, gained by using a restricted

sweeping range in the same experiment, is also illustrated in the lower panel of fig.

10.

The in-beam counting rate of the electron spectrometer depends on the position of

the momentum window. In this experiment, at the lowest field used (B\ — 0.0364 T),

corresponding to an electron energy range of 100 — 160 keV, with 25 nA beam current,

the counting rate was ~ 5 kHz. It drops with increasing magnetic field mainly because

of the E~7 energy dependence of the -electron production cross-section.

As can be seen in fig. 10, the energy resolution for the 386.8 ktV K line was about

2.6 keV (FWHM). One can compare the peak-to-background ratios in the simulta­

neously measured 7-ray and electron spectra. For the 386.8 keV$+ -* 6 + transition

the ratios are 13 : 1 and 7 :1 , respectively. (Details of the spectroscopic results are

found n ref. [21].)

17

An example of spectroscopy of electrons following the decay of high spin isomeric

states is shown in fig. 11. The nucleus 21*Ra has several isomers [22], whose life-times

vary from ~ 100 ns to ~ 67 ps. High spin states in n*Ra were populated using a

pulsed-beam and the ^Pty^CAn) reaction at 78 XttV. The 1 ns wide beam pulses

were separated by 4 ps. The target thickness was 2.5 mg/cm2. The electron spectrum

shown in the lower panel of fig. 11 was generated by setting an 800 ns wide time

window ~ 200 ns after the beam pulses. The component of the spectrum having a

longer life-time was removed by subtracting a spectrum obtained with a time window

~ 2.8 us after the beam pulse.

The upper panel of fig. 11 shows the spectrum in the "prompt" time region (—60

to +80 ns). Although some of the low energy transitions seen in the decay spectrum

have prompt components [22], the corresponding conversion lines are invisible in the

prompt electron spectrum. Most of the intensity (for example ~ 85% at ~ 1051teV)

observed in the low energy part of the prompt spectrum is due to j-rays. However

their intensity drops rapidly with time and 70 ns after the beam pulse the yield is

1/500 of the maximum. In this way it was possible to measure conversion electron

lines of relatively weak, delayed low energy (EK ~ 100 ArcV) transitions.

6. Summary

An electron spectrometer, consisting of a superconducting magnet transporter

and Si(Li) detector with envelope and anti-positron baffles, has proven successful in

the spectroscopy of conversion electrons following (HI,xn) reactions. Good energy

resolution, high momentum selection and background suppression enables the deter-

18

mination of conversion coefficients over a wide energy region. Computer control of

the lens-mode operation allows flexibility in the choice of the energy region covered

and consequent optimisation of efficiency, with a well-defined functional form.

Acknowledgements

We would like to thank R.J. Ball and J.D. Stewart for their valuable contributions

to the commissioning of the electron spectrometer, B. Fabricius and A.E. Stuchbery

who participated in some of the measurements, B. Fabricius also for his development

of the graphics system MULTIFIG, L.K. Fifield for the use of the program to control

the DAC, Professor A.R. Poletti for his encouragement and the academic and technical

staff of the ANU HUD accelerator facility for their support. The project was partly

funded by the Auckland University Research Grants Committee.

19

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Kleinheinz, Annual Report KFA Julich 1981, p. 130.

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Watson and P. Walker, Nuclear Structure Appendix to the Daresbury Annual

Report 1983/84, p. 110.

[ 8] P.J. Daly, Z.W. Grabowski, W. Trzaska, R.V.F. Janssens and T.L. Khoo, Ar-

gonne National Laboratory Physics Division Annual Reviw 1986-87, p. 159.

20

[ 9] A. Passoja. P. Tikkanen, A. Krasznahorkay, Z. Gacsi, T. Kibedi and T. Fenyes.

N-d. Instr. and. Meth. in Phys. Res. 223 (1984) 96.

[10] K. Vad. private communtication.

[11] B. Olsen, G. Petterson and W. Schneider, Nucl. Instr. and Meth. 41 (1966)

325.

[12] A.P. Byrne and G.D. Dracoulis, Nucl. Instr. and Meth. iu Phys. Res. A234

(1985) 281.

[13] V.A. Kuzminikh and S.A. Vorobiev, Nucl. Instr. and. Meth. 129 (1975) 561.

[14] M.J. Berger, S.M. Seltzer, S.E. Chappell, J.C. Humphreys and J.W. Motz, Nucl.

Instr. and. Meth. 69 (1969) 181.

[15] J. Deslauriers and S.K. Mark, Nucl. Instr. and: Meth. 159 (1979) 243;

G.G.Colvin and K Schreckenbach Nucl. Instr. and. Meth. in Phys. Res.

A228 (1985) 365.-'

[16] K. Farzin, K. Uebelgunn and H.von Buttlar, Nucl. Instr. and. Meth. in Phys.

Res. A240 (1985) 329.

[17] H.R. Faust, Nucl. Instr. and Meth. 213 (1983) 271.

[18] R.S. Hager and E.C. Seltzer, Nucl. Data A4 (1968) 397.

[19] M.J.L. Yates, in: Alpha-, Beta- and Gamma-ray Spectroscopy, vol. 2, ed. K.

Siegbahn (North-Holland, Amsterdam, 1965) p. 1691.

[20] C.A. Henry, private communication.

21

[21] G.D. Dracoulis. T. Kibedi, A.P. Byrne, B. Fabricius and A.E. Stuchbery, Nud.

Phys. A509 (1990) 605.

[22] A.E. Stuchbery, G.D. Dracoulis, T. Kibedi, A.M. Baxter, A.P. Byrne. B. Fabri­

cius and A.R. Poletti (to be published)

22

Table 1

Lens spectrometer characteristics

calculated measured

momentum window

acceptance angles a )

paddle wheel baffle transmission

maximum transmission

maximum efficiency **

momentum resolution (Ap/p)

11 s -32°

73%

6.67% of 2*

5.69% of 2x

0.12

5.9(5) % of 2T

0.12(1)

energy-field relationship coefficients'*

*-* lower

Cupper

0.260

0.290

0.325

0.2566(3)

0.2891(3)

0.3217(3)

solid angle attenuation factors

Ga(e)

Q*(e)

0.820

0.483

a) with respect to the soienoid axis

b) less than the transmission because of the electron detector response

c) eq. (6)

23

Table 2

Typical values of the K electron angular distribution function (WK(Q) ) for pure

transitions in Osmivm.

[kcV]

HV(6)->

[kcV] El Ml E2 M2 E3 [kcV]

6 = 90* 0* 90" 0" 90- 0* 90* 0* 90* 0*

200 0.861 1.277 1.002 0.995 0.774 1.508 0.804 1.381 0.787 1.428

500 0.920 1.159 1.019 0.962 0.809 1.361 0.813 1.345 0.806 1.387

1000 0.971 1.057 1.030 0.941 0.825 1.296 0.818 1.324 0.812 1.376

1500 1.011 0.979 1.036 0.928 0.829 1.279 ...

0.821 1.312 0.814 1.373

a) For dipole transitions: Afh) = -0.20, Affr) = 0.0,

for quadrupole transitions: Afd) = +0.35, A f f r ) = -0.10

and for stretched E3 transitions: Af{i) = +0.45, A'fb) = 0.0

were assumed.

24

Figure captions

Fig. 1. Coil and terminal arrangement of the solenoid. Magnetic field (Bz) profiles

(measured: ooen circles; calculated: lines) along the solenoid axis are obtained

with a current of 24.833 A across terminals 1—2 (curve a) and 3 - 2 (curve o).

Schematic drawing of the two-loop baffle system a shown in the lowest panel.

(B - axial baffle, D - diaphragm , APB - paddle wheel (anti-positron) baffle.

The envelope" of the electron trajectories are also shown.)

Fig. 2. Electronic block diagram.

Fig. 3. ExperimentaI(open circles) and calculated (solid line) momentum windows for

the 344 keV K line of inEu as a function of the magnetic field.

Fig. 4. Magnetic field-energy dependence determined for the momentum windows (fig.

3) for the conversion lines of inEu. The solid lines have been fitted to experi­

ment (dots).

Fig. 5. High energy region of the electron spectrum measured with a inTa source.

Fig. 6. Experimental swept efficiency determined using conversion electron lines and

the continuous 0~ spectrum of li7Eu. The curve was obtained by a fit of eq.

(10) to the experimental values (dots with error bars).

Fig. 7. Conversion electron and continuous ^"-spectrum of I M £ u source. The fitted

spectrum of the strongest ^"-transitions (see in the text) are displayed with

dashed lines.

Fig. 9. Verification of the calibration of the 7- and electron spectrometers.The ratio of

known conversion coefficients (oJfw*n ) to experimental values {0%* ) is shown.

25

Fig. 9. Illustration of the momentum selection in an in-beam measurement. The elec­

tron spectra shown correspond to equivalent collection times.

Fig. 10. Gamma-ray and conversion electron spectra measured in the 1 6*£>( 1 60,4n) 1 8 OOs

reaction [21]. The lowest panel shows the restricted range measurement which

results in enhanced efficiency.

Fig. 11. Prompt and delayed electron spectrum of 2URa produced in the 2 0*P6(1 3C,4n)

reaction.

26

- i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — r - 1 — > — i — i — i — > — ' — > — ' — i — i — ' — ' — " — i — r

1.0 -

a) terminals 1-3 b) 2-3

0.5

0.0

short end 1 3

m target long end

S S S |

target

2

beam APB

1 ' • • ' ' • ' • ' ' • • • • ' • • • • ' •

-200 -100 100 z [mm]

200 300 400

Fig. l

27

S i ( L i )

GE

HALL PROBE

BEAM CHARGE

Jl GDG

2 OR MASTER

GATE

VZ-.

MASTER SCALER

FAST AMP V

CFD

FRCH CCMPTON SUPPRESSOR

5 — 1 »

GDG

"kz. FAST AMP

V CFD

Jl ANTI,

R KP—»4

COIN

AMP €-»

i>

- T n s

*1 DELAY ^ FAN-IN

C h

~ y FAST VETO [J"

AST » | jOGIC

GDG STROBE

START'

STOP

TAC

AMP

ADC I

£5 ADC 2

ADC 3

V X level n

ISOL. AMP

X MP

LINEAR GATE

GATE JT_

DAC :SCL. AMP

CONTROL POP 11

-*j READ

X level

LINEAR GATE

A GATE

fc-»

_TL

A X 4

A X S

TO SOLENOID POWER SUPPLY CONTROL

Fig. 2

28

T — i — i — i — | — i — i — r

dp

~ 4 u c <D

•H O

-H 4-1

3 -

1—'

B

T J 1 1 1 T

max

J i__i

0.050 0.055 0.060 B [T]

0.065 0.070

Fig. 3

29

o

0.20 -

0.15 -

« 0.10 -

0.05 -

0.00

••—useful energy region

• • •

500 1000 electron energy [keV]

IS

Fig. A

30

600 T — i — | — i — i — i — i — J — r — i — i — i — | — i — r I ' • '

500

400

CO +J c a o o

300

200

100 ^ » ' • « ^ o r- r- ^«

• • • • 00 <S\ t—• ^r CN UO o ^* <T\ o> o o

182 Ta electrons 1121.3 i n

0 800

1157.3 + 1158.1 i n

1189.1 i ~n

1221.4 i n

1231.0 Tl

« « 1289.2

?>• nif A i

900 1000 1100 electron energy [keV]

1200 1300

Fig. 5

31

10

>

W CO

5 -

\ conversion lines A Fermi-Kurie plot

J i i i i i i • ' • I I L

500 1000 electron energy [keV]

15(

Fig. 6

32

/

10° E 1 r T 1 1 r I f

10'

10c

io 3

: 122

B io 4

I 10*

10<

101

10L

152£U ic electrons and p~-rays

— fitted P spectrum

245 344

• • I I L 500 1000

electron energy [keV] 1500

Fig. 7

33 f

1.5

• • i i I i i i i I i i i i

J l 5 2 E u T i a 0 o s l 2 0 6 B i £ 2 0 7 B i j209p o £ 2 1 0 t o £ 2 1 1 * § 2 1 % ^212^

a I 0

8

1.0 L T-*-»T T t fl t i " -r1

0 5 i • • • • i i . . . i • .

0 500 1000 transition energy [ktV]

1500

Fig. 8

1A

T 1 r

10'

10-CO -p c 3 o o 10'

10-

10 o IL

T 1 I 1 1 1

1 6 8 E r + 87 MeV 1 6 0 electrons

momentum selected background

j i L J I L 500

electron energy [keV] 1000

Fig. 9

35

7

i i i i ; i i i i | i i r i | i i i i | i i i • | i i i i | i i i i | i i i i | i i—r—r

60

40

276.8 180, Os gannas

132.5

20 I

u Ci3 oo

386.8 <T\

- \ I I I I I I I 11 I I I I I M I

2 so vo

i n OJ

o

mvo f-4VO

$¥ yk .m

^ » o % ^ » on vo vo I I

QO

ir> CM OO'

3C CD OO

CO

CNJ O cr>

I

rrTiTrrh'pi i r i*ri >

CO

o CO

c 3 o

15

10

•132.5

184.3

electrons

Bx - 0.036 T

B 2 - 0.251 T

276.8 i n

825.4 902, i n i I I K I | I I I I | I I I I

15

10 386.8 462.9 i ni n 510.6

1 1 I 1 I I I I• 1 l r tl I I 1*1 I

electrons

B x » 0.062 T

B2 » 0.118 T

8 -"n . H-

430.2 i n

n 541.5

566.6 644.5[SO) 584.2[E0)

699.2(E0)

i 11 f

r

J — L

100 • • ' • • • • ' ^ ' •

200 300 -1_L_L

400 500 600 700 transition energy in Os [keV]

Fig. 10

900 1000

36 /->

500 1000 electron energy [keV]

Fig. 11 17 ;;