The INFN exam for nuclear and subnuclear physicists, to select 58 new researchers, took place on September 19th (first test) and 20th (second test) in Rome. Two different locations for the two tests were set up as the number of candidates who enrolled in the selection were 720, a too large number to manage in a single location.

Having some experience of this kind of exams, I wrote a few blog posts here, aimed at training would-be researchers with typical questions - or at least, ones that I would have put in a selection test if I had been one of the examiners. You can find these at the following links: 0, 1, 2, 3, 4, 5, 6, 7, 8.

Now INFN finally made public the text of the exams. It is in Italian, so I thought I would translate a few parts of it for you.

The first test, which had to be completed in 4 hours, contained 20 mandatory questions plus a set of other 40. Among the latter each candidate had to pick 20 to give an answer to. So in total there were 40 answers to give in 4 hours, for an average of 6 minutes per answer. 

An additional feature was the fixed space that each candidate was given to produce his or her answer: this was pretty small, with typically only three or four lines of text allowed. This had the purpose of reminding the candidates that they had to be quick and to the point (and of making the evaluation task simpler).

Here are the 20 mandatory questions.

1) How does the power emitted by a relativistic particle of energy E and mass m in motion in a circular orbit (e.g. in a synchrotron) depend on E/m? Indicate some applications or relevant consequence of this emission. (use max 3 lines for the answer)


2) How much energy does a 1 GeV electron lose by traversing a material of thickness corresponding to one radiation length? (use max 2 lines)


3) What is the purpose of quadrupoles in a particle accelerator? (use max 2 lines)


4) A 400 GeV/c muon enters vertically into the sea. Through what physical process can it be detected? Estimate the depth at which it penetrates and decay. (use max 4 lines)


5) A scintillator emits 10,000 fotons per MeV. Compute the resolution (FWHM) that can be obtained for particles of 4 MeV assuming a 100% light detection efficiency. (use max 3 lines)


6) One observes that 2500 measurements of a quantity x are normally distributed. From these values one obtains an average of <x>=34.00+-0.06 (68%CL). What is the probability that in one further measurement a value x>37 is obtained ? (use max 3 lines)


7) In what energy region are located the X rays characteristic of the K series of elements from Oxygen to Uranium? (use max 2 lines)


8) What is the range of 60 MeV protons in a soft biological sample? What is the main therapeutic advantage of oncologic hadrotherapy with respect to tradiational radiotherapy? (use max 4 lines)


9) A cylindrical proportional tube has a radius R, the wire has radius r and the tension applied is V. Express the value of the electric field at a distance d from the tube axis. (use max 2 lines)


10) A pure beam of K_L mesons traverses a thin foil of material. Why can one find downstream a beam with a significant K_S component? (use max 2 lines)


11) A nucleus A alpha-decays to a nucleus B with a mean life t_A=2 minutes. B decays into C with mean life t_B=5*10^3 seconds. We start with N_A=2.7*10^7 A nuclei. Compute the activity of B after 1.2 seconds and after 5*10^3 seconds. (use max 3 lines)


12) Why is neutrinoless double beta decay possible only for Majorana neutrinos with non-zero mass? (use max 2 lines)


13) An excited state of 57Fe decays emiting a 14.4 keV photon (with half-life of 68ns). Determine the FWHM of the energy distribution of the photon. (use max 2 lines)


14) Indicate which among the following EM transitions are allowed in electric dipole approximation (E1) or in magnetic dipole approximation (M1): 1/2+ -> 1/2- ; 0+ -> 0-; 3/2+ -> 1/2-; 2+ -> 1+; 1+ -> 0+. (use max 1 line)


15) Indicate the composition in terms of valence quarks and antiquarks for a baryon, a meson, a tetraquark, and a pentaquark state. (use max 2 lines)


16) In a circular ring of 300m length circulates a beam of antiprotons of 6 GeV/c momentum and total current of 0.16 mA. The beam crosses at everyturn a gaseous hydrogen target with surface density of 10^14 atoms per square centimeter. Compute: a) the revolution frequency; b) the number of antiprotons; c) the integrated luminosity in 6 minutes. If one wanted to obtain the same CM energy in a proton-antiproton collider, what should the beam energy be? (use max 4 lines)


17) Why is a semiconductor diode used as a radiation detector normally inversely polarized? (use max 2 lines)


18) The J/psi resonance has a mass of 3096 MeV and a width of about 100 keV. Why is it so narrow?  (use max 2 lines)


19) The LEP dipoles allowed a maximum magnetic field of B=0.135 T and covered 2/3 of the accumulation ring of 27 km. What was the maximum energy one could achieve for the accumulated electrons? (use max 4 lines)


20) One wants to study the properties of a system with linear dimension d=1 fm by an electron beam. Estimate the minimum required beam energy. (use max 3 lines)

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The other 40 questions were on a mix topics: subnuclear physics, nuclear physics, detector physics, accelerator physics, theory, and astrophysics. I have no stamina to translate them for you, but if you want to examine them please download the original text here.

The second test, on September 20th, was to be completed in 2.5 hours. The candidates had to write a composition following very strict requirements. Here is the translation of the stipulation:

Illustrate in synthetic and quantitative way, following the listed scheme, a research activity in experimental physics of interest of INFN: a measurement, or a development of detectors, of accelerators, of technologies or of applied methodologies.


1. Scientific objective
2. State of actual knowledge of the topic
3. Instrumentation and/or required technological developments (described if needed with schematic drawings)
4. Data analysis
5. Synergic technologies or measurements
6. Comparison with competing experiments or activities
7. Description of expected results and/or possible consequences
8. Perspectives, developments or long-term improvements


If you do not consider necessary to discuss one or more of the above points, motivate the choice.



I will be happy to hear your comments on the above tests, and discuss whether such a method to select 58 researchers (from a pool of 720 applicants) is sound or can be improved, and how. [Note that these two written tests are only a part of the selection process: candidates are ranked also based on their CV, their publication record, and an oral interview.]