MANUAL FOR THE ANALYSIS OFCLARA-PRISMA DATA

Non puoi insegnare niente a un uomo; puoi solo aiutarlo a scoprirlo in se stesso.

Galileo Galilei

You cannot teach a man anything; you can only help him find it within himself.

Galileo Galilei

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This short manual is intended to be a support for the CLARA-PRISMA user.The single steps of the calibration of the different kinds of detectors that constitutethe complex CLARA-PRISMA set-up are described in section 1, while the dataanalysis is presented in section 2.

The procedure here explained is meant to be software independent. Howevercommands and features, useful for the users who intend to perform the analysisusing the gsort package, are highlighted in boxes. The commands are not explainedin detail. A description of each command can be obtained using the gsort help.

Additional appendices on the gsort package are included.

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1 Procedure for Detector Calibration

In this first section we describe the main steps required for the calibration of thestandard CLARA-PRISMA detectors.

In appendix B you will find the header for the typical gsort setup file and thedescription of the presort procedure that can be used to speed up the analysis.

1.1 MCP Calibration

In this section we will present the procedure to calibrate the MCP start detector ofPRISMA [1].

Firstly a 2D gate (also called ‘banana gate’ in the following) is needed to cut offbad events from MCP, see Fig. 1.

Figure 1: Raw data from MCP with the 2D gate defining the good events.

Figure 2 shows the MCP matrix in coincidence with the focal plane of thePRISMA magnetic spectrometer. This coincidence is needed to visualize the ref-erence cross, which is placed behind the MCP detector itself [1]. In the figure thenumbers refer to each of the five possible calibration reference points, representedby rectangular ticks on the cross. Number 1 refers to the centre of MCP. Addi-tional useful reference points are two screws located in the dipole, that were usedto assemble the magnet itself and were then left in situ.

The MCP detector presents non uniformities. This is seen in the lack of alignmentof the reference points in the MCP cross, see Fig 2. Therefore, before calibratingthe MCP signals we need to align these reference points.

We need to ”deform” the signals to align the reference points. In the examplereported in the box later on in this section the deformation is achieved by a linearcombination of X and Y signals. This is just anm example and the user can develophis own procedure.

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1

2

34

5

Figure 2: Raw data from the MCP detector after applying the previously defined2D gate and requiring the coincidence with the focal plane of the PRISMA magneticspectrometer. The lack of linearity of MCP is clearly visible comparing the referencepoints (represented by the lines). The numbers refer to each of the five possiblecalibration reference points. Number 1 refers to the centre of the MCP detector.

Figure 3: Aligned reference points after deformation and rotation.

In addition to the deformation, in some cases, it is required to rotate the MCPdetector around its centre. This is needed if the shadows of the two screws that canbe seen in fig. 2 are tilted. Usually the screws are tilted at very small angles (2-3degrees). The result of these two actions can be seen in Fig. 3.

After these steps, we can calibrate in mm the X and Y signals from the MCPdetector. The calibrated position of the ions at the entrance point is needed to per-form the tracking of the ions within PRISMA (in the case of gsort, this informationis passed to the routine PRISMA SOLVER, see section 2.1).

The coordinates of the points in the laboratory reference frame of CLARA-PRISMA are listed in table 1.

As one can easily see the calibration of the MCP signals according to these

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Reference point X coordinate in LAB (mm) Y coordinate in LAB (mm)Point 1 0 0Point 2 -430 530Point 3 -430 -530Point 4 430 -530Point 5 430 530

Table 1: True coordinates of the five reference points shown in Fig. 2.

Figure 4: Spherical coordinates in the PRISMA (left panel) and in the beam (rightpanel) reference frame. The numbers in the right panel show the coordinates ofthe centre θ = 49.0◦ (the grazing angle where PRISMA was placed in the presentexample), φ = 90.0◦.

reference points requires a mirrowing of the image with respect to a vertical axispassing through the centre of the MCP: points 2 and 3 are in the right part offigure 2 but their coordinates place them on the left side. No symmetrization isinstead required for the y axis.

Figures 4 show the MCP detector in spherical coordinates in the laboratory (thePRISMA reference frame) and in the beam frame of reference (left and right panelrespectively).

If using the gsort code for data analysis, the routine grazing mcp will calculatethese quantities.

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∗ A0 represents the X coordinate∗ A1 represents the Y coordinate

∗ selection of good eventsbanana A0 A1 good event.ban Res 4096 4096 IN

∗ coincidence with Focal Plane of PRISMAgate R4 10 4095 in 1 10

∗ Syntax to get the alignment of the reference points:add A0 A1 A4 Fact 1 -0.005351309 Gain 1.0 off 0.00add A1 A0 A5 Fact 1 0.035351309 Gain 1.0 off 0.00

copy A4 A0copy A5 A1

∗ Syntax to rotate the MCP detector in its own reference frame,in the case∗ this is needed. In the example a rotation of 2.5◦ is applied.rotate mcp A0 A1 A0 A1 2.5

∗ Calibration of MCP:

gain A0 2159.278 -0.64576 1 4095 1 1gain A1 -548.86 0.697437 1 4095 1 1

∗ At this point you get the MCP signals calibrated as follows:∗ A0 = A0*20 + 1000 mm∗ A1 = A1*20 + 1000 mm

∗ Syntax of the command that converts from cartesian coordinates∗(A0 A1) in the laboratory frame to spherical coordinates in the∗ laboratory (A2 A3) and in the beam frame (A4 A5) of reference.∗ The last number is equal to the angle at which PRISMA is placed∗ (the grazing angle).

grazing mcp A0 A1 A2 A3 A4 A5 49.0

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1.2 MWPPAC calibration

The MWPPAC [2] focal plane detector of PRISMA gives 6 sets of signals:

• Up position;

• Down position;

• Left position;

• Right position;

• Cathode;

• TOF.

The first two informations are common to the 10 sections of MWPPAC and areused to extract the Y position. This information gives an idea of the centering ofthe beam.

Since the MWPPAC detector is divided in the X direction into 10 sections, theLeft, Right, Cathode and TOF signals are registered for each of them.

Left and Right are used to extract the X coordinate information by subtraction.

Figure 5: Left+Right (y axis) vs. Cathode (x axis ). Requested Banana selectinggood events.

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In order to eliminate noise signals in the cathode a first poligonal gate on amatrix Right+Left vs. Cathode is required, as it is shown in fig.5.

Even if not essential for the following analysis one can consider the option of firstaligning the 10 cathode signals. This will result in a cleaner picture and an easierselection of good events. One can instead decide to create 10 individual bananas,one for each section.

Figure 6: Right-Left (y axis) vs. Cathode-Left (x axis)

Owing to inefficiencies it can happen that for some events one of the two signals(Left or Right) is missing. This is particularly true in the case of light ions. Inorder to recover the statistics one can relate the signal from the cathode to eitherLeft or Right and extract the final X position. This is achieved by performing thefollowing calibration: first of all one should calculate the difference Cathode-Leftand Right-Cathode and then display them against the XFP signal calculated in thestandar way (Right-Left. An example of such dependence is shown in fig.6 in thecase of Cathode-Left. A similar picture will be obtained for Right-Cathode. A linearcalibration is therefore obtained by extracting the slope and offset of the lines.

This calibration has to be calculated for each different section of the MWPPACseparately.

If using the gsort code for data analysis the command XFP PRISMA willdirectly combine the three signals (Left, Right and Cathode) given the cali-bration parameters extracted as specified before.

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Figure 7: Fully reconstructed XFP

At this point one can calibrate the XFP position in mm, applying the calibrationcoefficients provided by the local support group. A typical calibration file can beseen in appendix C. The resulting spectrum should be similar to fig.7. Differencesfor different reactions are expected.

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∗ R0, R1 Up, Down∗ R2 Left∗ R3 Right∗ R4 TOF∗ R5 Cathode∗ Ri section id

∗ MWPPAC signals 6= 0gate R0 10 4070 IN 1 1gate R1 10 4070 IN 1 1gate R2 10 4072 IN 1 10gate R3 10 4072 IN 1 10gate R4 10 4072 IN 1 10gate R5 10 4070 IN 1 10

∗ Remove cathode noise:∗ Sum of Left and Right signal. gain =0.5 is used to keep the picture∗ within 4096 chs.add R2 R3 R0 gain 0.5sort3d Ri R5 R0 Id Cat Left+Right Res 16 4096 4096∗ Need to define a banana for each section of the MWPPACbanana R5 R0 2D-gate Res 4096 4096 in 1 10

∗ Evaluation of the relation btw. Cathode and Left/Right.∗ NB: these lines are required only when defining the calibration for XFP .∗ Then they will be commented out using ∗add R5 R2 R0 fact 1. -1. gain 0.5 offset 2000. ∗ Cathode-Leftadd R3 R5 R1 fact 1. -1. gain 0.5 offset 2000. ∗ Right-Cathodeadd R3 R2 R6 fact 1. -1. gain 0.25 offset 2000. ∗ Right-Leftsort3d Ri R0 R6 Id Cat-Left X Res 16 4096 4096sort3d Ri R1 R6 Id Cat-Right X Res 16 4096 4096

∗ Calculation of XFP using Left, Right and Cathode informationsXFP PRISMA R2 cal-file R3 cal-file R5 NORUN 0.00 1.00 1 4090 1 10

∗ Calibration in mmrecal R2 cal-file NORUN 0.00 0.100 1 4090 1 10

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1.3 TOF calibration

The TOF signal is registered in TACs started by the cathodes of the MWPPACdetector and stopped by the MCP time signal. We therefore have 10 separate TOFsignals which have to be aligned one respect to the other. In order to better visualizethe 10 signals it can be useful to create a 2D matrix where the TOF is plotted againstthe XFP . An example of such a matrix is shown in fig.8.

Figure 8: TOF vs. XFP before aligning the individual sections

One has to correct for drifts occuring during the experiment: this is achieved byshifting the position of the main peak to the initial position for each different run.

The TOF has an arbitrary offset that has to be corrected. The easy way of doingthis is to make use of a matrix where the TOF is plotted against the quantity D/R,being D the total distance covered by the ions and R the curvature radius of thetrajectory of the ions. An example of such matrix is shown in Fig. 9. In this matrixone can see different lines corresponding to different masses and different chargestates, all of which should pass from the origin of the coordinate system. This doesnot happen ususally and therefore one should calculate which is the common offsetthat has to be subtracted. The procedure to extract the quantities D and R isexplained in the section 2.1.

At this point one is able to calibrate the TOF signal usually in tenths of ns,thanks to the calibration file that the local support group will provide. A typical

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Figure 9: TOF (y axis) vs. D/R (x axis). A common offset for these lines has to beextracted.

calibration file can be seen in appendix D. The resulting matrix should look like theone in fig.10.

if using the cmat program to visualize this matrix the common offset isautomatically obtained simply by drawing a banana around the lines andusing the command Y that calculates a common intercept and slope.

One can now check whether the TOF corresponds to the predicted value andcorrect for the required offset (if required). This check can also be done based onthe speed (v/c) that is calculated as it is explained in section 2.

The fine adjustment of the offset of the TOF can be performed by making useof the Ge energy spectra: after applying the Doppler correction to the Ge spectra(see section 2) we can check that the main lines have the correct energy and width.

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Figure 10: TOF vs. XFP after alignment and calibration in tenths ofns. Note thatthe direction of the time axis is now reversed.

For this check, in order to clean the spectrum, it can be useful to set a gate onthe Z of the channel corresponding to inelastic excitations of the beam. Usually oneselects this channel since this is the most intense one, and since its transitions areusually well studied. For details on the Z selection procedure see section 2.2.

This fine adjustment is an iterative procedure that will end when the user issatisfied with the accuracy in defining the peak energy and width. We cannotdefine a standard limit since this strongly depends on the energy of the transitionand the speed of the ions, but an easy calculation can help defining the expectedvalue, at least for the width.

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∗ TOF is identified with variable R4

∗ Alignment of the 10 sections:recal R4 cal-file NORUN 3700.00 -10.000 10 4000 1 10

∗ Alignment of each section within runs:recal R4 runs-cal-file RUN 0 1.0 10 4000 1 10

∗ Definition of the common offset:∗ After the command PRISMA SOLVER∗ F3 is R and F9 is D∗ gain = 100 is used to expand the figure, otherwise compressed in few chs.divide F9 F3 F9 gain 100.0 offset 0sort2d F9 R4 common offset Res 4096 4096

recal R4 cal-file NORUN 0.00 1.000 10 4090 1 10

∗ optimization with Doppler correction∗ fine gaingain R4 32. 1. 1 8192 1 10∗ after the procedure in sec 2.1 F7 is β.∗ after the routine grazing mcp A2 and A3 are the angles∗ in PRISMA reference frame. Q3 is the HPGe energy.

recal polar Q3 F7 A2 A3 CLARA 0 1 10 8192 1 100

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1.4 IC calibration

The ionization chamber (IC) of PRISMA [2] is divided into 40 sections: 10 padsin the X direction (in exact correspondance to the ones in the MWPPAC detector)each of them divided in depth into 4 sections. Additional side pads are used inanticoincidence mode to suppress ions whose trajectory escaped laterally. Each padacts as an independent ∆E section.

The calibration of the IC is done applying the coefficients provided by the localsupport group. This will not give an absolute calibration of the signals in MeV, butwill only result in the correct alignment of the signals from each PAD.An example of such a calibration file is given in appendix E.

∗ The ionization chamber is identified with detector I

∗ Suppression of trajectories giving signals in side pads is achieved∗ imposing fold = 0 for the side detector, identified with the letter S

fold S 0 0

∗ Calibration of the 4 rows of pads using given calibration file:

recal I0 I0-Cal-file NORUN ZERO 0.000 1. 0 8191 0 10recal I1 I1-Cal-file NORUN ZERO 0.000 1. 0 8191 0 10recal I2 I2-Cal-file NORUN ZERO 0.000 1. 0 8191 0 10recal I3 I3-Cal-file NORUN ZERO 0.000 1. 0 8191 0 10

1.5 Ge calibration

The calibration of the energy spectrum/a of Ge detectors is performed in the usualway by making use of standard radioactive sources (60Co,152 Eu,56 Co and others ifavailable and required by the user). Gainmatching of the energy signals does notseem to be required but one can easily check it by plotting the energy spectrum indifferent runs. Similarly one should carefully check the drifts occuring in the timespectra.

Usually one requires an anticoincidence with the Anti-Compton shields and,after the proper calibration is applied, the addback of signals occuring in adjacentcrystals.

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∗ Anti-Compton shields are variables Q0 (energy) and Q1 (time)∗ Rejection of events in which the Anti-Compton shields firedgate Q0 0 10 in 1 40

∗Calibration of the three informations of Ge detectors:∗ Q2 20 MeV ADC∗ Q3 4 MeV ADC∗ Q4 TDCrecal Q2 cal-file-20MeV NORUN ZERO 0.00 1.00 1 8191 1 100recal Q3 cal-file-4MeV NORUN 0.00 1.000 10 8191 1 100recal Q4 cal-file-Time NORUN 0.00 1.000 10 8191 1 100

∗ Gate on time spectra to reject randoms (not very effective, though)gate Q4 2230 2261 in 1 100

∗ Addbackaddback Q2addback Q3

∗ Combination of 20 and 4 MeV signalscombine Q3 Q2 Q3 LIMIT 3800

∗ Doppler correction of the energy spectra. F1 is the v/c, A0 and A1 are∗ θ and φ angles calculated in the PRISMA reference framerecal polar Q3 F1 A0 A1 CLARA 0.00 1.0000 10 16384 1 100

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2 Analysis

Beyond the specific aim of each experiment, once every physical signal coming fromthe detectors has been calibrated, one has to reconstruct the trajectories of the ionsthrough PRISMA in order to determine atomic and mass number of the reactionproducts. Additional information can be found in Ref. [3]

2.1 Trajectory Reconstruction

PRISMA provides a set of information, which allows the reconstruction of the tra-jectory of each single ion, namely:

• the spacial coordinates in the entrance detector (MCP);

• the spacial coordinates in the focal plane detector (MWPPAC);

• the time of flight (TOF) between MCP and MWPPAC ;

• the energy released in every single section of the ionization chamber (IC).

From these information one can extract the following quantities:

• the length of the trajectory;

• the curvature radius of the trajectory in the field of the dipole magnet;

• the total energy released in the ionization chamber;

• the range of the ions in the IC.

In gsort the reconstruction subroutine treats the quadrupole and the dipolemagnets as ideal magnetic elements. Since border effects are relevant, they’re takeninto account making use of an effective length for the quadrupole, greater than thereal one.

The concepts upon which the PRISMA SOLVER routine is based are described inappendix F.

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The PRISMA SOLVER routine is used to calculate the trajectories withinPRISMA. The routine calculates the following quantities:

• Azimuthal, θ, and zenithal, φ, angles in PRISMA frame of reference(F1, F2);

• the path length of the ion (F9);

• the curvature radius in the dipole magnet (F3);

• the total energy released in the ionization chamber (F4);

• the range of the ion in the ionization chamber (F8, F7).

In order to do that PRISMA SOLVER needs to be provided of:

• the calibrated spacial coordinates of the MCP entrance detector (A0,

A1);

• the square root of the ratio between the dipole and the quadrupolemagnetic fields (0.956077 in the example). This is to be calculated bythe adc converter program;

• the effective length of the quadrupole (420.0) and the distance betweenthe target and the quadrupole (540.0);

• the energy released in each section of the IC (I0, I1, I2, I3);

• the calibrated XFP (R2).

The syntax for this command is the following:PRISMA SOLVER F1 F2 F9 F3 F4 F8 F7

A0 A1R2 0.956077 420.0 540.0I0 I1 I2 I3 10.0

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2.2 Z identification

The energy-loss by ionization of charged particles traversing matter, namely the gasin the ionization chamber, is described by the Bethe-Bloch formula:

dE

dx∝ MZ2

E(1)

Plotting the sum of the energies released in each row of the IC (total energy) versusthe energy lost in the first row one can disentagle different atomic species, as inFig. 11.

Figure 11: ∆E vs E matrix showing the different Z’s.The most intense line corre-sponds to the beam.

It can be useful, in particular in the case of heavy species, to plot, as ∆E, thesum of the energies lost in the first two rows and not only in the first row.Another way to select the atomic number is to plot the Range versus the TotalEnergy, as shown in Fig. 12. Sometimes this gives a better separation of the differentZ’s. Range and Total Energy are calculated by the routine PRISMA SOLVER.2D banana gates are therefore applied to select the different species and proceedwith the mass identification independently for each Z.

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Figure 12: Range on x axis vs Energy on y axis.

2.3 A/Q and mass identification

In the previous section we selected nuclei having a certain atomic number, but themass of each ion has not been recognized yet. Since more than one charge state isusually transmitted to the focal plane, a procedure to disentangle the different A/Qis needed.

The motion of the ions in the magnetic field of the dipole magnet is ruled by theLorentz force:

mv2

R= qvB (2)

Where m is the mass of the ion, v its velocity, q its charge state, B the magnetic fieldin the dipole and R the curvature radius of the trajectory followed by the isotopein the dipole.

From eq. (2) it’s possible to extract the A/Q ratio of the different nuclei, ex-pressed as:

A

Q∼=

m

q=

BR

v(3)

The quantities which have to be calculated are therefore the radius R, given bythe routine PRISMA SOLVER, and the velocity v. The velocity of the nucleus is simplyobtained as the ratio between the path length and the TOF , that leads to:

A

Q=

BRD

TOF

(4)

where D is the path length from the MCP entrance detector to the focal planedetector, again calculated by PRISMA SOLVER. Most of the times reactions may pro-

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duce ions having a velocity around or greater than 10% the value of the speed oflight in vacuum. For this reason it’s wise to use the relativistic expression of theLorentz force, obtained just by substituting in eq. (4):

TOF = TOF√

1 − β2 (5)

being β = vc.

∗ What follows is an example of how β can be calculated according to∗ equations (4) and (5).∗ F9 is the path length, D, R4 is the TOF∗ the factor 0.03335641 is obtained measuring c in mm/tenths of ns

add F9 F0 F0 Fact 0.03335641 0.copy F0 F1∗ F0=F1=D/c

power F1 2.0 Gain 1 Offset 0.∗ F1 = (D/C)2

mean R4 F3power F3 2.0 Gain 1 Offset 0.∗ F3 = (TOF )2

add F3 F1 F4 Fact 1. -1. Offset 0.∗ F4 = (TOF )2 − (D/C)2

power F4 0.5 Gain 1∗ F4 = sqrt((TOF )2 − (D/C)2)

divide F0 F4 F7 gain 100. offset 0.∗ F7 is now D/(c ∗

√

(TOF 2 − (D/C)2)) = β = v/c∗ F7 is β in %

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Plotting A/Q versus the X position in the focal plane one should see straighthorizontal lines. If these lines are not aligned in the different sections of the focalplane a realignment of A/Q is needed, as shown in Fig. 13.

Figure 13: XFP on x axis the value RV

proportional to AQ

on y axis.

∗ Procedure to get a 2D spectrum A/Q vs X, as in Fig. 13.add R0 F7 R0 Fact 0. 1.∗ R0 is now F7 that is D

c√

(TOF 2−(D/c)2)

= β

divide R3 R0 R5 Gain 15. offset 0.∗ R5 is R

V, proportional to A

Q

∗ Sorting of a matrix with X position on the focal plane on the x axis∗ and A

Qon the y axis

sort2d R2 R5 XFP AQ Res 2048 4096

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Fig. 14 shows the projection of Fig. 13 on the A/Q axis. The most intense peakscorrespond to the inelastic scattering of the beam for different charge states.

Figure 14: Spectrum of the different A/Q, the most intense peaks are the beaminelastic excitations in the different charge states.

In order to disentangle the different charge states, and eventually obtain themass of the ions, one should consider that from eq. (2) and from

EIC =1

2mv2 (6)

one can obtain the following equation:

EIC ∝ qRv (7)

Therefore, it’s possible to disentangle different charge states plotting EIC versusRv. An example of such spectrum is shown in Fig. 15.

Once the selection of the charge states is performed, one can calibrate the spec-trum in Fig. 14 in order to have a correspondance between the channel number andthe value A/Q. Making use of many programs, it is possible to calculate the mostprobable charge states that are transmitted to the focal plane of PRISMA. One hasthen to associate the value of Q to the correct banana applied to Fig. 15, and thencalculate the ration A/Q.

An explicatory example: in the reaction 48Ca+64Ni at a beam energy of 280 MeVthe most probable charge state is 18+. The most intense peak in Fig. 14, which is theinelastic scattering of the 48Ca beam, should therefore be positioned in the channel:

A

Q=

48

18= 2, 667 (8)

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Figure 15: Rβ, proportional to A/Q,on X axis versus the total energy released inthe IC.

A similar ratio is then calculated for all the charge states. A recalibration of theA/Q axis is performed.In this way, when plotting a mass spectrum, one directly gets entire mass values.

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∗ Procedure to get a calibrated mass spectrum.mean R3 F12∗ R3 and F12 are the curvature radius

mult F12 F1 F11 Offset 0. Gain 0.25∗ F11 is 0.25 ∗ R ∗ β and it’s proportional to a RV

add R1 F11 R1 Fact 0. 1.add R0 F4 R0 Fact 0. 1.∗ R1 is proportional to the curvature radius times the velocity,∗ R0 is the energy released in the IC

gain R5 -258.15 1.89209605 10 8192 1 1∗ the previous gain command is used to calibrate A/Q values

pin R1 R0 F13 R7 R6 3 Res 4096 8192 1 11 1 190 ./Ca191 2 180 ./Ca181 3 170 ./Ca17

mult R5 R7 R6 gain 0.01 offset 0.∗ R6 is now the value of the mass in A

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Appendix A

The gsort sorting code is part of the package EGASPWARE. This package containsalso other programs, such as cmat and xtrackn, useful for spectra handling.

The EGASPWARE package can be downloaded from the docserver of LNL(http://www.lnl.infn.it/docserv/) logging in in read-only mode and going under thedirectories Gamma and then PRISMA.

Please download the last available egasp TGZ archive.Unzipping and untaring is simply obtained by the command:tar ZXVF archive-name

The package contains an already compiled version of the programs. Compilationof the package is not usually required. If needed, the installation procedure and thesystem requirements are described in the file INSTALL.

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Appendix B

Here we report an example of the header for a typical CLARA-PRISMA setupfile. Each detector is labelled by a letter. The order is the same stated in the firstline after the word PRISMA.

format PRISMA Clover Titris Trigger Monitor MCP PPAC IC ICside Dante

cdetector Q 25 2 8192 8192 SEG 4 3 8192 8192 8192detector T 1 4 16384 16384 16384 16384detector J 1 3 16384 16384 16384detector M 3 1 4080detector A 1 4 4080 4080 4080 4080cdetector R 1 2 4080 4080 SEG 10 4 4080 4080 4080 4080detector I 10 8 4080 4080 4080 4080 4080 4080 4080 4080detector S 2 8 4080 4080 4080 4080 4080 4080 4080 4080cdetector D 1 3 4080 4080 4080 SEG 8 4 4080 4080 4080 4080

if you plan to perform a standard analysis, as the one desribed in this manual,in order to play the files quicker it can be useful to presort them into shorter filescontaining only the essential information.

Here we report an example of a setup file used for presorting.

format PRISMA Clover Titris Trigger Monitor MCP PPAC IC ICside Dante

cdetector Q 25 2 8192 8192 SEG 4 3 8192 8192 8192detector T 1 4 16384 16384 16384 16384detector J 1 3 16384 16384 16384detector M 3 1 4080detector A 1 3 4080 4080 4080cdetector R 1 2 4080 4080 SEG 10 4 4080 4080 4080 4080detector I 10 8 4080 4080 4080 4080 4080 4080 4080 4080detector S 2 8 4080 4080 4080 4080 4080 4080 4080 4080cdetector D 1 3 4080 4080 4080 SEG 8 4 4080 4080 4080 4080

gate R4 100 4070 in 1 10banana A0 A1 ../gates/MCP x-y Res 4096 4096 IN 1 1

WRITE EVENT D R 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 00 0 0 0 0 0 0 0 0 0clover titris Trigger Monitor MCP PPAC IC ICside Dantebreak

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After such reduction one needs to use a different header for the setup file. Hereis an example of an header suitable for the data format defined in the previousexample.

format GASPheader F PLUS 14 8192 8192 8192 8192 8192 8192 8192 8192 8192 8192 8192 8192 81928192

cdetector Q 25 2 8192 8192 SEG 4 3 8192 8192 8192 PLUS 1 16384detector M 3 1 4080detector A 1 3 4080 4080 4080 PLUS 7 4096 4096 4096 4096 4096 4096 4096cdetector R 1 2 4080 4080 SEG 10 4 4080 4080 4080 4080 PLUS 7 8192 8192 8192 81928192 8192 8192detector I 10 4 4080 4080 4080 4080detector S 2 4 4080 4080 4080 4080

useful F10 F0 F1 F2

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Appendix C

Example of the calibration file used to calibrate the XFP position in mm. Eachline refers to a different section. A linear ( 2 coefficients) calibration is applied inthis example.

0 0 2 -664.556 0.5812810 1 2 359.345 0.5669590 2 2 1326.52 0.5882860 3 2 2340.3 0.5811220 4 2 3302.23 0.5972970 5 2 4318.74 0.5940930 6 2 5328.1 0.5900840 7 2 6317.57 0.5941080 8 2 7357.15 0.5701130 9 2 8353.31 0.576428

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Appendix D

Example of the calibration file used to calibrate the TOF position in tenths of ns.

1 0 4 -9.8097 0.093752 -1.2957e-06 1.9973e-101 1 4 -9.6032 0.097718 -3.4337e-06 7.025e-101 2 4 -9.5741 0.095725 -3.2349e-06 6.7583e-101 3 4 -6.3768 0.092982 -1.3987e-06 2.0825e-101 4 4 -4.8689 0.095879 -2.8322e-06 5.7765e-101 5 4 -4.5626 0.095399 -2.8372e-06 6.4036e-101 6 4 0.25314 0.0929 -6.4139e-07 5.5139e-11

1 7 4 0.010144 0.093019 -1.6603e-06 3.1317e-101 8 4 -0.68887 0.094529 -2.3179e-06 5.1759e-101 9 4 -2.5441 0.094395 -2.9086e-06 6.4507e-10

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Appendix E

Example of the calibration file used to calibrate the IC pads.

1 0 2 -48.66 1.0741 1 2 -40.77 1.0431 2 2 16.99 1.0241 3 2 -42.49 1.0361 4 2 -125.7 1.0861 5 2 -51.24 1.0681 6 2 -93.94 1.0631 7 2 -95.28 1.0721 8 2 -43.47 1.0611 9 2 -31.61 1.04

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Appendix F

Strategy applied in the PRISMA SOLVER routine to calculate the trajectory of theions:

Assuming an ideal magnetic quadrupole, the motion of a particle entering witha para-axial trajectory is fully determined by its magnetic rigidity and by the max-imum magnetic field. The same applies to the motion in an ideal magnetic dipole.

Given the curvature radius in the PRISMA dipole, the ratio of the fields in thedipole and in the quadrupole and the entry point in the start detector of PRISMA,the motion in the quadrupole (and in the full PRISMA) can be determined asfollowing:

1. straight line from target to quadrupole entrance

2. motion in the quadrupole up to its exit

3. straight line to the dipole entrance

4. arc of circumference in the horizontal plane to the dipole exit

5. straight line in the horizontal plane to the focal plane

It should be remarked that the effect of the fringe fields is reabsorbed withan effective quadrupole length (which is therefore different than the geometricalquadrupole size). The iterative procedure performed within the FindTrajectory

public method starts by assuming a guess value R=120cm corresponding to thecentral trajectory. If the calculated point in the focal plane lies within a millimeterfrom the observed point, the iteration ends; otherwise it continues with a new guessvalue.

Assuming that the Ionization Chamber is divided in sectors (horizontal direction)and sections (depth), the present treatment is the following:

1. check if the sectors/sections which fired are compatible with the reconstructedtrajectory. The event is rejected if more than one section/sector outside thetrajectory is firing.

2. construct the energy deposition in each section by summing over the sectors.

3. construct a weighted section-PPAC distance, using the energy depositions ineach section as weights; an estimate of the range of the ion in gas is obtainedfrom this weighted distance, subtracting the PPAC-IC distance (in vacuum)

4. the final range estimates are obtained by manipulating the range obtainedabove exactly the same way as in the TRACK PRISMA subroutine.

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Notes: The geometry of PRISMA is read from a configuration file. The magneticfields are calculated from the values set in the power supplies using the same codedeveloped for the actual objects.

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Appendix G

Here is a list of the most useful gsort commands available. The syntax of eachcommand can be obtained by running gsort and writing the following line:

??name-of-the-command

FOLD Discard event if number of detectors outside limitsGATE Gate on a parameterGATES Multiple Gates on a parameterWINDOW Gates on all parameters of the defined typeBANANA 2-dimensional gateBANANAS Multiple 2-dimensional gatesFILTER Assign score acording to a filtering functionXBAN Exclusive 2-dimensional gate

RECAL MULT Recalibration of a parameter on different regions. Coefficientsfrom fileGAIN Change gain of a parameterRECAL Recalibration of a parameter. Coefficients from fileRECAL LUT Recalibration of a parameter from look-up tableTIME REFERENCE make time spectra with respect of one detectorTIMING make time spectra taking first coincidence as referenceRECAL DOPPLER Doppler correction with recoil-velocity function of gamma-energyRECAL KINE Kinematic reconstruction of G0 according to ISISTIME ADJUST Improve the timing by adjustment of the time referencePIN Particle Identification Number according to ISISHK Total energy H and Fold k of a detector (e.g. BGO ball)

ADD Add [with factors] 2 parameters into a 3rd oneKILL Kill detectors from the eventSELECT Select events with defined detectorsSTORE EVENT Save a copy of the event in its present statusRECALL EVENT Recall the saved copyWRITE EVENT Write events to Tape or Disk file in (reduced) GASP formatLIST EVENT List events on TerminalREORDER Order the sequence of detectors of the eventSTATISTICS Calculate the statistics of detectors

SWAP Swap two parametersMASK Binary mask of a parameters

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MOVE Move a list of detectors of one type into another typeMERGE Merge detectors togetherSPLIT Split detectors from one type to a list ofNEWID Change the id of detectorsEBKILL Selective kill of Euroball detectorsCOMBINE Combines 2 parameters togetherADDBACK Addback of composite Euroball detectorsCOPY Copy one detector or parameter into anotherUSEFUL Put Run#, Record#, Event# and Count# in header parametersTHRESHOLDS Eliminate out-of-range values for a parameter. Threshold valuestaken from file

MULT Multiply 2 parameters into a 3rd one with gainMEAN VALUE Put in a header parameter the mean value of the given detectorparameterDIVIDE Divide 2 parameters into a 3rd one with gain ( P1/P2 -¿ P3 )ESL TO ECM Calculate the energy value in CM (nonrelativistic)RECAL CHOOSE Recalibration of two parameters, choosing the best value for thefirst oneWMEAN VALUE Put in a header parameter the weighted mean value of the givendetector parameterRECAL POLAR Doppler correction with recoil-velocity and polar anglesRECOIL VEL Extract recoil velocity vector from Si-detector signalsANGLES PRISMA Calculate polar angles and theta for particles detected withPRISMA spectrometerTRACK PRISMA Track trajectories in PRISMA spectrometerQVALUE PRISMA Calculate Q-value for binary reactions (PRISMA/CLARAsetup)BP VELOCITY PRISMA Calculate velocity vector for the unobserved particle inbinary reactions (PRISMA/CLARA setup)XFP PRISMA Pre-process focal-plane X coordinate for PRISMA spectrometerPRISMA SOLVER Track trajectories inside PRISMA spectrometer in a transparentwayROTATE MCP Rotate MCP start detector around its centreGRAZING MCP Extract angles in LAB and BEAM reference frame from MCPcoordinatesXFP IC Extract X coordinate of the PPAC from IC signals

BREAK Stop event analysis, ignore the comands following itPAIRGATE Gate on parameter asociated with pairs of detectorsPOWER Raise one parameter to a given power

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PROJECTIONS Projections for all defined parameters and detectorsSORT1D 1D sort of any parameterSORT1D M 1-D multiple sort with HGATE

SORT2D 2-D sort of any pair of parametersSORT3D 3-D sort of any triplet of parametersSORT4D 4-D sort of any quadruplet of parameters

SORT2D AB 2-D sort of one detector with different parameters on the 2 axis

SORT2D SYMM Symmetrized 2-D sortSORT3D SYMM Symmetrized 3-D sortSORT4D SYMM Symmetrized 4-D sort

SORT3D PAIR 3-D sort of Pn-Pn-Pair indexSORT3D DIFF 3-D sort of Pn-Pn-Difference

SORT2D HSYMM Half-Symmetrized 2-D sortSORT3D HSYMM Half-Symmetrized 3-D sortSORT4D HSYMM Half-Symmetrized 4-D sort

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References

[1] G. Montagnoli et al., Nucl. Instr. and Meth. A547 (2005) 455-463.

[2] S. Beghini et al., Nucl. Instr. and Meth. A 551 (2005) 364-374.

[3] A. Gottardo, Diploma Thesis, http://clara.pd.infn.it/thesis/thesisGottardo.pdf.

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