PhD in Theoretical and Computational Physics: Rotational Invariants for X-ray Imaging at European XFEL (75%)

PhD in Theoretical and Computational Physics: Rotational Invariants for X-ray Imaging at European XFEL (75%)

How much structural information can rotational invariants recover from X-ray patterns when particle orientation, background and missing detector regions complicate interpretation? This three-year European XFEL doctorate combines mathematical inverse problems, scientific programming and experimental data. It offers an identifiable research lineage in rotational invariants and single-particle imaging, with public software and datasets. The central institutional question is which university will award this doctorate and who will act as academic supervisor: European XFEL is the employer and research facility, not an identified degree-awarding university. The official vacancy gives 23 November 2026 as its closing date. The 75% position pays €3,676.28 gross monthly for 29.25 paid hours a week; the degree route and personal employment terms still need confirmation.

Research work and what would make it a doctorate

The Theory group seeks methods for scattering and single-particle imaging of biological and nanoengineered particles. The advertised tasks are to develop rotational-invariant approaches, extract and analyse angular cross-correlation functions, interpret experimental XFEL datasets—primarily from European XFEL—and participate in relevant beamtimes and collaborations. The candidate will contribute to in-house structural-analysis software and publish results, present at conferences and write a PhD thesis. This is a new doctoral research route requiring a Master's, rather than a short visit restricted to already enrolled doctoral students. Research duties and entry qualification.

Individual diffraction patterns contain orientation, background, detector gaps and limited signal. Rotational invariants encode structural information while removing rotational degrees of freedom, allowing statistical correlations across patterns to inform reconstruction or forward models. That does not eliminate every inverse-problem ambiguity or make every fitted structure unique. The recent workflow uses harmonic expansions, constrained iterative phasing and alignment/averaging; the virus study addresses real masks, noise and regularisation. Those are concrete examples of the mathematics and numerical validation the doctorate may build on, rather than a promise of one fixed algorithmic deliverable. Reconstruction workflow; Experimental invariant analysis.

For preparation, a useful small project would reproduce part of an available correlation/reconstruction workflow, then examine sensitivity to background, missing detector regions or model assumptions. This is an applicant suggestion, not an employer-approved plan. Ask which biological/nanoengineered systems and datasets are committed, which problem needs a new theoretical contribution, how success will be evaluated, and how software maintenance, beamtime participation and independent thesis work are divided. The role includes contact with experiments; it is not described as an entirely remote coding position. Project scope.

People, software and recent research

Dr Ruslan Kurta is the advertised scientific contact and is listed as a theoretical physicist in the Theory group. The official group page names Alexander Lichtenstein as group leader and separates European XFEL staff from University of Hamburg staff. This supports a genuine joint scientific environment, but does not name Lichtenstein as this opening's academic supervisor or make Kurta a university professor by inference. Clarify daily mentoring, the academic signatory and the complete supervisory arrangement. Scientific contact; Theory group membership.

The public xFrame project documents a Python-based analysis framework; the 2024 paper describes NumPy/SciPy, harmonic/Fourier transforms, lower-level C/Fortran routines and OpenCL acceleration, with HDF5/YAML inputs and outputs. These give applicants realistic preparation targets. The public GroEL dataset includes raw runs, calibration information, masks, rotation lists and structural models. Neither public resources nor facility-scale infrastructure confirms the new student's allocated compute/GPU budget or access to particular unpublished datasets. xFrame documentation; CXIDB187 dataset; Software implementation.

Three recent original studies involving Kurta clarify different parts of the inverse problem. Reading covers selected methods, results and limitations from their full HTML sources; supplementary derivations and datasets were not comprehensively audited:

Berberich, Molodtsov and Kurta (2024): reconstruction workflow

Berberich, Molodtsov and Kurta, 2024: a workflow extracts invariants, performs iterative phasing and aligns/averages reconstructions in xFrame. The demonstrations use ideal noise-free simulated data, dilute-particle assumptions and 10⁵ patterns per model. Convergence metrics do not directly measure distance from experimental truth. It is a strong software/methods foundation, without establishing robustness under all real beamtime conditions. Journal of Applied Crystallography paper.

Berberich and colleagues (2026 preprint): real-data limitations

Berberich and colleagues, 2026 preprint: model-guided and ab initio analysis of aerosolised PR772 viruses uses difference-pattern correlations, masks, Fourier methods, regularisation and xFrame. Three historical LCLS experiments supplied 3069, 5030 and 221 selected patterns. Reconstructions reveal departures from ideal capsid symmetry and possible internal/vertex features at limited resolution. Rapid aerosolisation/vacuum effects cannot be excluded, so these observations do not prove unperturbed native-state dynamics. It is labelled an arXiv preprint here, not assumed peer-reviewed, and its historical data location must not be confused with the new job's mainly European XFEL datasets. 2026 original manuscript.

Ekeberg and colleagues (2024): protein diffraction and background

Ekeberg and colleagues, 2024: the team observes interpretable diffraction from an approximately 14 nm GroEL protein complex at European XFEL's SQS instrument. Template/background analysis compares about 4.3 million simulated patterns and reveals how much apparent intensity comes from background. The X-ray signal reaches roughly 6 nm resolution and the phase-retrieval map is too coarse for further structural conclusions; this is not an atomic-resolution 3D protein structure. The 4.6 Å map discussed elsewhere in the paper is a cryo-EM reference. Additional density cannot be uniquely identified as water at the X-ray resolution. This provides a concrete reason to take background and model validation seriously. Light: Science & Applications paper.

University, discipline and doctoral training

Employer: European XFEL GmbH, Theory group, Holzkoppel 4, Schenefeld, Germany. Awarding university for S-685: not named in the current advert. The employer's programme describes fully funded three-year PhDs and cooperation with partner programmes; the 2026 training update says candidates are associated with several universities, with Hamburg the largest German partner. It announces plans to strengthen doctoral training through a doctoral school, which does not prove that a new self-awarding institution is already operating. Exact employer; Doctoral programme; June 2026 training update.

The 2023 programme guidelines describe a university agreement signed by the academic supervisor, local supervisor and student, annual progress arrangements, and reporting of courses/graduate-school membership. Only the relevant indexed sections were recovered. Their special provision for an exceptional extension in the R&D-funded subset does not establish which funding bucket S-685 uses or create an entitlement to a fourth year. The current public curriculum offers voluntary programming/data and writing workshops and an annual student presentation day; additional graduate-school credits must be checked with the school/supervisor. A fixed doctoral-credit total, defence rules or university-specific language threshold cannot yet be assigned to this post. Programme guideline sections; Curriculum.

If Hamburg is the agreed university, its Physics procedure provides an actionable foreign-degree route: Master's degrees obtained outside Germany, outside Physics or at a university of applied sciences require pre-review. Academic admission must be sought before starting the doctoral project, with a supervision agreement, research outline, degree/transcript records, identification and other prescribed documents; foreign Master's candidates supply thesis title/abstract and certified translations where necessary. Admission and subsequent university enrollment are separate. These are verified Hamburg procedures, not confirmation that S-685 has already secured Hamburg registration. Physics doctoral admission; Foreign/external-project pre-review; Enrollment.

European XFEL should not be assigned a university league-table rank. For conditional partner context only, ShanghaiRanking lists Hamburg ARWU 2026 overall 201–300 and GRAS 2026 Physics 101–150. They are Hamburg's indicators and neither an XFEL ranking nor a confirmed ranking of this job's degree route. Decide primarily from the actual scientific work, mentoring and eventual academic agreement. Provider profile.

Employment, salary and costs

The exact vacancy specifies 29.25 hours/week, a 75% position, limited to three years, with PG13/1 at €3,676.28 per month. The salary is already for 75%; do not reduce it again or advertise a 100% salary. The employer's pay policy identifies remuneration as gross monthly salary. Confirm the start date, payroll treatment and any subsequent step/tariff change in the contract. The advert does not promise renewal. Ask how the part-time paid hours relate to expected doctoral work and beamtime schedules. Current salary and duration; General gross-pay framework.

The advert offers an annual special payment of 75–95% of one month's salary depending on pay group, a company pension scheme quoted at 6.45% of monthly salary, partial Deutschlandticket support, relocation benefits and 30 paid vacation days plus 24/31 December. Work-from-home options depend on tasks; family support, subsidised language/sports offers, staff events, a discounted restaurant and mental-health support are also listed. These benefits do not establish a net take-home calculation. The general salary page still gives a different 60–90% bonus range, so the current vacancy should guide the offer discussion and the exact PG13 rate must be confirmed. Position benefits; Generic policy discrepancy.

The PhD programme says non-German candidates hired from abroad receive an international allowance. A generic salary page mentions at least 15%, but the exact job does not specify a personal amount or eligibility calculation. Treat it as a concrete HR question rather than automatically adding 15% to base pay. Likewise, relocation support requires actual terms; neither full personal-cost reimbursement nor guaranteed housing is established. Doctoral international benefits; General allowance policy.

Hamburg's 2025 qualified rent survey reports €9.94/m² net cold rent, referenced to 1 April 2025 and released 9 December 2025. This describes the relevant existing rental stock in Hamburg: it is not a furnished new-listing price, warm rent or a Schenefeld-specific offer. Schenefeld is the workplace in the wider metropolitan area. Budget against actual accommodation and commuting options, adding utilities/heating, deposit, food, insurance/social deductions, tax and household needs. The university's housing guidance confirms that affordable housing is difficult and services cannot guarantee a contract; access to university services itself depends on affiliation. City rent survey; Researcher housing guidance.

Fees depend on the eventual university. If enrolled at Hamburg, general tuition has been abolished but semester contributions remain; the published winter 2026/27 general contribution is €402, and doctoral first-semester enrollment requires the full contribution. Future semesters and any personal exemption need confirmation. These are conditional costs, not proof that every S-685 candidate pays exactly €402 or that every charge is reimbursed. Tuition distinction; Current semester contribution; Doctoral enrollment payment.

Qualifications and application

The exact requirements are a Master's in Physics or a related discipline, a strong mathematical background, programming ability, spoken/written English and communication skills with interest in collaboration across theory and experiment. Python or C/C++ is an asset, while programming itself is required. The advert does not specify a minimum grade, a numerical IELTS/TOEFL result, German proficiency, prior beamtime experience or an existing doctoral enrollment requirement. Academic degree equivalence and additional university language requirements still depend on the degree route. Selection criteria.

A convincing application should show mathematical reasoning and a research-oriented programming project, ideally with reproducible validation, rather than only a list of languages. Fourier/harmonic methods, linear algebra, inverse problems, noise/background analysis and numerical experiments are preparation priorities inferred from the actual papers; they are not extra mandatory criteria added to the advert. Show that you can communicate physical assumptions and limitations to experimental collaborators. Mathematical and software example; Real-data analysis.

The official application asks for CV and motivation letter in English, plus any reference letters, through the online recruitment system. No mandatory three-referee count or fixed proposal length is stated for this opening. The employer page confirms 23 November 2026; the earlier listing specifies 23:59 Europe/Berlin, so avoid last-minute submission. Scientific questions go to ruslan.kurta@xfel.eu; general recruiting questions can go to HR. Candidates with disabilities receive preference over otherwise equally qualified applicants. Application instructions.

Chinese-applicant feasibility and constraints

Positive evidence goes beyond a generic international label: European XFEL publishes a procedure for non-EU employees hired from outside Germany, and its PhD programme explicitly addresses non-German recruits abroad. The German government's research-visa guidance includes third-country doctoral candidates completing a thesis under an employment contract at a research facility. Suitable foreign academic qualifications may provide access; the host/authority must decide the actual residence category. A full-time study programme can instead require the study route. The employer's older webpage contains 2021 Blue Card numbers that should not be used as current eligibility thresholds. Employer non-EU recruiting route; International PhD benefits; Government doctoral-worker route.

If Hamburg is chosen, its explicit foreign-Master's pre-review offers a further positive academic pathway for a Chinese degree, subject to equivalence and any additional requirements. This does not mean Hamburg admission, a visa or facility access has been granted. The exact advert names no China-specific or other nationality exclusion and no special security-clearance requirement. General export rules remain distinct from that absence: BAFA's guidance defines basic-research scope narrowly rather than exempting every academic activity. Any actual data/code/equipment restriction requires an institutional assessment, not a blanket inference about Chinese applicants. Foreign qualification procedure; Pre-review; Current advert scope; BAFA scope excerpt.

Career and transferable skills

The likely portable skills are scientific software, image reconstruction, statistical/numerical modelling, reproducible analysis and collaboration at large research facilities. Plausible routes include photon-science research, imaging/algorithm R&D and scientific computing. Germany's official research-career guidance describes both non-university research and company R&D paths; it does not establish job counts or placement rates for this narrow specialism. The physics problem is specialised, but the numerical skills are broader if the thesis includes well-tested software and transferable methodology. Research career framework; Implemented workflow.

Questions and next steps

Before applying: ask which university/department and academic supervisor will take responsibility for the degree, whether registration can be arranged for a foreign Master's, and what additional grade/language documents are required. Confirm the start date and funding of the full three years. At interview: define the first dataset/particle system and new mathematical question; ask about compute allocation, code responsibilities, beamtime participation, mentoring, progress milestones and a fallback if new data are delayed. Discuss paid hours versus doctoral workload. Before accepting: obtain the academic/local agreement, admission timetable, fees, base pay/bonus/allowance/pension details, relocation terms and personal residence/access requirements in writing, and check a real housing budget. This is a credible new doctoral research opportunity; the remaining degree-route details deserve resolution before treating its academic outcome as fully confirmed.

Evidence and Sources

The saved employer vacancy gives 23 November 2026 without a cutoff hour; an earlier EURAXESS listing gives 23:59 Europe/Berlin. The exact cutoff and current availability remain unconfirmed. Publication stages and reading limits for the three papers are stated above; policy, tariff, rent and semester figures retain their source dates and do not establish personal terms.

Position, people and training

• European XFEL official S-685 theoretical and computational physics doctorate
• European XFEL Theory group members
• European XFEL doctoral programme funding and international benefits
• European XFEL PhD Student Programme Guidelines June 2023
• European XFEL doctoral curriculum
• European XFEL June 2026 doctoral training update

Research, software and data

• A workflow for single-particle structure determination via iterative phasing of rotational invariants in fluctuation X-ray scattering
• Imaging aerosolized viruses with an X-ray free-electron laser using single-particle rotational invariants
• Observation of a single protein by ultrafast X-ray diffraction
• xFrame official project documentation
• CXIDB187 GroEL single-protein diffraction public dataset

Conditional university route

• University of Hamburg Physics doctoral admission procedure
• Hamburg Physics foreign-degree and external doctorate pre-review information
• Hamburg doctoral enrollment and semester contribution
• Hamburg winter 2026/27 semester contribution
• Hamburg tuition and semester contribution distinction
• ShanghaiRanking Hamburg 2026 profile: conditional university context

Salary, costs and international feasibility

• European XFEL support for nonEU recruits hired abroad
• German government visa for research and employed doctoral candidates
• European XFEL general salary and benefits policy
• Hamburg official 2025 qualified rent survey
• Hamburg international researcher housing guidance
• German government research careers and international employment
• BAFA export control and academia: basic research scope