POLARIZATION MEASUREMENTS OF TWO He I TRANSITIONS USING BEAM-TILTED-FOIL EXCITATION

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POLARIZATION MEASUREMENTS OF TWO He I TRANSITIONS USING BEAM-TILTED-FOIL

EXCITATION

R. Brooks, E. Pinnington

To cite this version:

R. Brooks, E. Pinnington. POLARIZATION MEASUREMENTS OF TWO He I TRANSITIONS

USING BEAM-TILTED-FOIL EXCITATION. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-

295-C1-297. �10.1051/jphyscol:1979161�. �jpa-00218441�

JOURNAL D E PHYSIQUE Colloque C1, supplgment au no 2, Tome 40, fgvrier 1979, page C1-295

POLARIZATION MEASUREMENTS OF TWO He I TRANSITIONS USING BEAM-TILTED-FOIL EXCITATION*

R. L. Brooks and E. H. Pinnington

Department of Physics, University of Alberta, Edmonton, Canada T6G 251

~ 6 s u m 6

-

Les paramstres de Stokes de la lumisre Emise aprss excitation faisceau-lame ont 6t6 mesur6s pour les transition 2s 'S

-

3p 'PO et 2p 'Po

-

4d 'D de He I en fonction de l'angle d'inclind

son de la lame de 00

2

800 par pas de 5O. Les courbes obtenues de cette fa on sont bien dif-

f -

fgrentes pour les deux transitions. Ces mesures sont une extension d'une exp6rience site recement qui a d6montr6 3e bon accord entre les paramstres de polarisation des transitions 2s

-

3p et 2s

-

4p et entre ceux des transitions 2p - 3d et 2p

-

4d.

Abstract

-

The Stokes parameters of light emitted following beam-foil excitation have been measured as a function of foil tilt angle from O0 to 80°, in 5 degree increments, for the 2s 'S - 3p 'Po and 2p 'Po

-

4d 'D transitions in He I. The curves so obtained are remarkably different for the two transitions. These measurements are an extension of a recently completed experiment which demonstrated the close agreement be- tween the polarization parameters from the 2s

-

^{3p and 2s}

-

4p transitions and between those from the 2p

-

^{3d and 2p}

-

4d transitions.

1.INTRODUCTION

-

Recently we have presented the polarization measurements as a function of foil tilt angle for four transitions in neutral Helium (2s IS- np 'Po and 2p 'Po

-

^{nd ID; n = 3,4).l} The measure- ments were taken at 10 degree increments, from O0

to 70°, and were able to demonstrate the qualitative agreement between transitions differing only in

. . I

.L . , c l r

- .

prir.cipa1 quantum zumb~r. The results, hcw-

ever, showed a marked dissimilarity between the 'S

-

1 ^PO transitions and those from 'Po

-

^{ID. When}

the results were compared to a recent theory,2 the

'S - 1 ^{P O} transitions gave good agreement while the

'pO

-

1 D transitions did not.

It was clearly desirable to repeat these measure- ments, for at least two transitions, to try to establish a trend through as large a foil tilt angle as possible. We here present the Stokes parameters for the 2s 'S

-

^{3p 'PO} (50161) and 2p 'Po

-

^{4d D} 1 (49221) transitions in He I taken with the foil tilted from O0 to 80' in 5 degree increments.

2.EXPERIMENT

-

Several modifications were made to the target chamber following the experiment reported in Ref. 1. The beam diameter was reduced from 7 mm to 5 mm. Two sets of foil holders with elongated apertures (5 x 10 mm & 5 x 15 mm) were constructed.

The foil tilt mechanism was altered to permit 5 deg- ree tilt increments from 00 to 80'.

Figure 1 illustrates the beam, foil and detector geometry used for this experiment. Two fused silica lenses of equal focal length were employed to focus light at 90' to the beam onto the entrance slit of a 314 m Czerny-Turner Spex monochromator. The two- lens configuration ensures parallel light passes through the polarimeter which consists of a quartz

arizer. Either of these may be rotated by a step- ping motor with reproducibility of axis position of 0.1'. The entrance and exit slits of the monochro- mator were tilted to remain parallel to the foil up to 60'. The entire spectrometer rests on a movable table which may be adjusted for proper focus at any measurable wavelength.

Our methods for data acquisition and experimental control have been previously described.' Nominally 5 ug/cm2 carbon foils were used at a beam energy of 160 KeV. The beam current was maintained at 7 f l p A for all measurements except the 75' and 80' foil tilt angles for which the current was 4 + 1 uA. Op- tical normalization utilizing the He I1 line at 4686

6:

was employed throughout. Data were acquired by rotating the quarter-wave retarder before a fixed polarizer in 10 degree increments through a sweep of 360'. Typically, five such sweeps were summed to comprise one data sample.

3.DATA ANALYSIS

-

The Stokes parameters can be completely determined by rotating a quarter-wave retarder before a fixed polarizer, thus eliminating

zero-order retarder followed by a calcite prism pol- Figure 1. Beam, £011 and detector geometry

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979161

C 1-296 JOURNAL DE PHYSIQUE

0 20 4 0 60 80 Foil Tilt Angle ( a )

Figure 2. Stokes parameters vs tilt angle for He I 5016

2.

Smooth curves from equation (1) with A =

-5.18, B=-0.72, D=-3.05, E=-1.01 and F=0.16.

instrumental polarization entirely.3 Our method of data analysis differs from that of Berry et ala4 in that we employ a linear regression to obtain I, M, C and S after accurately determining the polarizer angle y , the retarder angle 6, and the retarder phase 6. These angles can be well determined by in- serting a second polarizer, Po, in front of the pol- arimeter. A carefully selected sequence of measure- ments with the polarizer in the polarimeter (P) in- serted both forward and backward at several different angles permits the evaluation of all three desired parameters (Y, B and 6). The crucial point is that the -relafive Stokes parameters, M/I, C/I and S/I must remain unchanged so long as Po is not altered.

Since the retarder phase, 6 , is a function of ' i

wavelength and needs to be evaluated for every line of interest, the measurement sequence will be des-

cribed in some detail. The second polarizer, Po, is set to O0 (the angle is not critical) and a data set is collected in the usual way with the polarizer, P , at 90° (crossed). P is then rotated through 90°

(aligned) and a second data set is acquired. The value of 6 is then varied in the analysis program until M / I for the two measurements agree. It happens that M/I for the aligned data set is a rapidly vary- ing function of 6 while for the crossed data set it is a slowly varying function. This feature permits self-consistency to be easily achieved with a preci- sion of one degree. By repeating the measurements several times, the accuracy can be as good as the precision. Further details of our data analysis methods are available elsewhere. 1

4.DISCUSSION

-

^Figure 2 shows our results for the 2s S -3p 'PO 1 transition at 5016

2.

Figure 3 shows the 2p 'PO-4d 1 D transition at 4922

g.

The ~"00th curves shown in the figures are from a least-squares fit of the results to a slightly modified form of Band's theory .2 The modification eliminated a

Foil Tilt Angle ( a )

llgure 3. Stokes parameters vs tilt angle for He I 4922

2.

Smooth curves from equation (1) with A =

-17.1, B = -0.36, D = 0.25, E = -0.69 and F = 0.19.

TABLE 1.

Po.eahization

a

04 He

_I

T/raMdUoMd

Foil Tilt 1

2s S

-

^{3p 'PO 50161 2p 'PO}

-

^{4d 'D 49222}

Angle (a)

(Degrees) M/I C / I ~ S/I M/ I c/lb S/I

0 16.8 20.8 -0.4 0.2 20.5 8.2 20.7

-

^{0.4 0.4 20.5}

5 17.2 20.8 -0.2

-

1.4 20.5 6.6 i0.7 0.0 0.2 20.5

10 17.9 20.8 0.3

-

^{3.3 f0.5 7.8f0.7 - 1 . 4 0.8 20.5}

15 16.5 20.8 2.1 - 5.2 20.5 6.6 20.7 - 1.2 0.4 20.5

20 16.0 "0.8 3.3

-

6.8 r0.5 6.0 "0.7

-

2.2

-

0.2 20.5 2 5 14.8 "0.8 3.7

-

8.9 50.5 5.4 20.7 - 2.6 0.0 k0.5 3 0 13.1 k0.8 3.1 -11.0 r0.5 5.0 i0.7

-

2.6 0.9 lt0.5 35 12.3 k0.8 2.7 -13.2 k0.5 3.1 C0.7

-

^2.7

-

^{0.4 i0.4}

40 9.8 20.7 3.3 -13.5 f 0.5 0.5 20.7

-

^2.8

-

^{0.8 f 0.5}

&5 7.8 20.7 4.0 -16.6 20.4

-

1.5 10.6 - 3.9

-

2.9 f 0.4 50 6.2 k0.7 3.8 -16.8 20.4 - 2.3 20.7 - 5.4 - 4.3 t0.5 5 5 4.1 "0.7 3.8 -18.4 f0.4 - 4.3 '-0.7 - 3.5

-

6.6 f0.5 60 0.6 "0.8 2.4 -18.8 20.5

-

7.7 20.7

-

^4.7

-

9.8 f 0.5 65

-

0.8 f 0.7 2.3 -20.5 C0.4 - 8.4 f0.6

-

5.8 -11.4 f0.4 7 0

-

^{5.1 20.8 0.8} -20.6 k0.5 -10.6 20.7

-

^5.1 -14.8 2 0.4 75 - 8.3 k0.7 -0.2 -21.5 f 0.5 -10.7 f0.7

-

^7.5 -15.6 C0.5 8 0 -10.6 20.8 -3.8 -22.9 lt0.5 -13.9 C0.8 -10.1 -19.8 10.5 a

-

values in percent

b

-

uncertainties same as M/I

redundant parameter and yields the equation:' the curious feature that for foil tilt angles less S sin a cos a

- -

1 - A cos2 a

+

B

than about 40°, S/I is essentially zero. This fac- tor, coupled with the change of sign of M/I at about

We have inverted the S/I results to determine A and B, then held these parameters fixed while determin- ing D, E and F from the C/I and M / I results.

One feature of the new data is that even at 800 foil tilt angle, S/I shows no indication of going to zero at 90° as predicted by the above equations.

This is probably indicative of the demand for higher order terms in the theory at large foil tilt angle and should not be interpreted as an in- trinsic failure of the theory. However, the 4922

2

data is not well followed by the theory with or

40°, causes a second marked feature not predicted by theory, a minimum in the total fractional polariza- tion Pf at about 40'. P is defined as

f ( M ~ +

c2

+ s2)5/1.

Our results are presented in Table I. The uncer- tainties are our best estimates of one standard deviation.

5.CONCLUSION

-

The Stokes parameters for two transitions in neutral Helium as a function of foil tilt angle have been presented. The marked dissimi- larity between the transitions caused mainly by an unusual feature of the 4922

2

line has been stressed. Ours is the first published data, of which we are aware, that has not been adequately described by Band's theory.

without the large angle points. This is because of

*

Work financially supported by the National Research Council of Canada and the Province of Alberta.

References

[I] R. L. Brooks and E. H. Pinnington, Phys. Rev. and Optical Measurement, Pergamon Press,

A, October 1978. Oxford, 1971.

[2] Yehuda B. Band, Phys. Rev. A,

13,

2061 (1976). [4] H. G:Berry, G. Gabrielse and A. E. Livingston, [3] D. Clarke and J. F. Grainger, Polarized Light Applied Optics,

16,

3200 (1977).